But they insisted last night they had yet to receive a credible offer from the Bluebirds for their bad boy striker.
Celtic, Fulham and Sunderland have all offered to take Bellamy on loan for the season and pay a chunk of his £95,000-a-week wages.
But Cardiff have only just had a transfer embargo lifted and there are serious doubts as to whether they can make an appealing offer.
Bellamy, 31, asked to go back to the family home as his relationship with Roberto Mancini unravels - and the Italian was happy to get the player out of his hair.
The Aston Villa midfielder is part of a £26million deal which includes City's £8m-rated Stephen Ireland joining Villa.
Both players have agreed personal terms but the deal is stalled as Ireland is still holding out for a £2m pay-off from City.
The saga has dragged on for over a week and Milner, 24, could call time on the move as he is desperate to avoid any more disruptions to Villa's season.
In a further twist, caretaker-boss Kevin MacDonald will pick him in his squad for Thursday's Europa League play-off at Rapid Vienna if the deal is not done.
And if Milner were to play, it would cup-tie him for City's own European campaign.
MacDonald said: "If James hasn't gone by midweek, I'm sure he'll want to play, because he just loves playing football."
Manchester City boss Mancini left Given, 34, on the bench and picked Joe Hart for Saturday's 0-0 Premier League draw.
Arsenal and Fulham are both interested in the Irishman - but Mancini hopes a Europa League outing against FC Timisoara will stop Given demanding for a move.
City defender Vincent Kompany admitted: "Joe and Shay are both world class, it's great to have either of them behind us.
"But I'm just glad it's not me who has to pick who plays."
The Welsh striker, 31, has fallen out with boss Roberto Mancini and wants to train with Cardiff.
Bellamy was informed over the weekend that he would not be welcome to join in with the first team squad at Eastlands.
So the Welshman asked for permission to keep himself in shape with his hometown side while he searches for a new club and his employers agreed.
Eastlands sources indicated last night they had not heard from Bellamy since - but their stance remained unchanged.
There is no ban preventing him from entering their Carrington headquarters but he will find himself marginalised if he does head back there.
Celtic, Everton, Sunderland and Fulham are all in the queue to snap up the player but City insist no bids are yet on the table.
Spurs boss Harry Redknapp finds it hard to believe Bellamy could end up at Cardiff.
Redknapp said: "He's a Premier League player in my opinion. No disrespect to Cardiff but he should be playing top Premier League football.
"Good luck to Cardiff but it would be a waste of an outstanding player.
"City paid a lot of money for Bellamy so why should they loan him?
"Someone will have to end up buying him, unless Man City loan him to a team like Fulham.
"Craig's a top player. He was outstanding last year. I tried to sign him when he left West Ham.
"I was in for him then but Manchester City beat us to him. But I've always been a big fan of Craig Bellamy's, he's a battler."
Stephen Ireland is expected to be used as a makeweight in the deal, which could be worth up to £22million.
Mancini said: "I hope we can close it between today and tomorrow. I think Milner is a good player, an English player — which is important. He can play in different positions."
Asked if the transfer would involve Ireland, Mancini added: "I hope so. We have today and tomorrow to close the deal."
Another player who could be heading for the Eastlands exit door is goalkeeper Shay Given — with Fulham lining up a bid if Mark Schwarzer completes a move to Arsenal.
Mancini added: "I hope Shay will stay with us because we are in four competitions but I respect his wishes if he wants to leave."
MILNER ... completed Man City move
The England midfielder has signed a five-year contract with Roberto Mancini's side in a deal which sees Stephen Ireland move in the opposite direction to Villa Park.
City boss Mancini said: "I am very happy to have James with us — everybody knows we have admired him for some time.
"He is an excellent midfielder, who can play in a number of positions.
"This is important for the team and I am looking forward to seeing him play for us. We have a very strong squad, and this signing is a very important one for us.
"James is already a very good player who has proved he can play at the very top level.
"But he is also young and a good character — I think he can also improve and be a great player for Manchester City for a long time."
Speaking on Ireland's departure, Mancini added: "I hope things go well for Stevie at Villa.
"He is also a very good player, and he has played a big part in City's history.
"I think he will enjoy the change of being at another club, and I hope he does well for Aston Villa."
Ireland said: "I have plenty of personal ambitions. I want to get back to playing the way I can — I haven't played 90 minutes in nearly eight or nine months, which isn't normal really for me.
"I've kind of forgotten the feeling what it is like to come off after a game feeling tired, winning or losing. I'm not used to sitting out for so long.
"So for me, I want to get back to playing at the top of my game and I want to work hard for my team-mates.
"I want to see if my team-mates and myself can push on and achieve something massive this season.
"Hopefully I can come here and build on that and help Aston Villa push on to better targets and reach higher goals. Hopefully I can be of benefit to the team.
"I think we have got a good bunch of young lads here who can go on and achieve something for themselves and for the club as well. We've got a very good squad."
Milner's drawn-out £24million switch from Aston Villa prompted a blast from Alex Ferguson, who criticised City's "kamikaze" spending.
But Eastlands boss Roberto Mancini used the unveiling of the winger to hit back at United.
He said: "I think all the other teams have spent a lot of money in the past. I don't mean 15 years ago but in the last one, two or three years.
"It is not important for me (what Ferguson says).
"But I repeat that Manchester United, like Manchester City, have spent a lot of money in the past."
Milner, 24, did not sign in time to join his new team-mates on their Europa League trip to Romania but set his sights firmly on the Premier League.
He said: "It didn't take too much selling by the boss when you see the players who are already here.
"The last thing he said to me was 'be ready to win the Premier League'.
"That's my ultimate aim - that's why I'm here."
The Romanian side are backed by oil magnate Marian Iancu.
And ahead of tonight's play-off first-leg he said: "My team will play for more money than the Manchester City players.
"Some can get to £82,000 if they help us beat them - they are ready to play the match of their lives."
City had to settle for Europe's second club competition this year after missing out on the top four by a point.
And Roberto Mancini's millionaires have become a prime scalp for the Romanian club.
Iancu - who owns UK-based Balkan Petroleum - bought the club back in 2004 and has spent around £24million assembling the squad, which finished fifth in the Romanian league last year.
That sum is tiny compared to the £325m spent by City's Arab owner Sheikh Mansour since August 2008.
Mancini: "This tie is important for me and the club and the supporters.
"The first game is always difficult."
The Slovakia international, who was also linked with Celtic, completed the switch earlier today in Glasgow.
Weiss, 20, is now set to go straight into the squad for Sunday's SPL clash with Hibernian at Easter Road.
That is HALF what Manchester City paid to sign the Brazilian striker from Real Madrid two years ago.
But if the move goes ahead and the player is a success, valuable add-ons worth another £10m could kick in.
Robinho's former Real coach Bernd Schuster is now in charge of Besiktas and would love to be reunited with the player.
Rivals Fenerbahce and German big-spenders Schalke are also interested - with Robinho keen on Turkey.
The former Aston Villa ace has won 11 caps but is not an established member of Fabio Capello's starting line-up.
He hopes his new boss Roberto Mancini will play him in the centre of midfield.
Competition will be stiff at City with Gareth Barry, Nigel de Jong, Yaya Toure and Patrick Vieira fighting for those spots.
But Milner said: "I enjoy it in the middle, that's probably my best position and I've played my best football there over the last 18 months.
"I've been at my most creative and I've scored goals. I've enjoyed it immensely there and I think that's where I've been signed to play.
"But if the boss asks me to play anywhere else, I'll do whatever is best for the team. As long as we're winning, that's all that matters.
"It might help my international chances. If you are playing week in, week out with good players, you are putting yourself in the window for England."
Milner hopes there will be no hard feelings from Villa supporters, who gave him a warm send-off in Saturday's 3-0 win over West Ham.
He said: "I loved every single second at Villa.
"Hopefully the fans know that every time I stepped out on the pitch I gave 100 per cent for them."
After initially launching their own cut-price negotiating service, the union now takes a five per cent cut of a player's contract.
And with former Aston Villa ace Milner set to pick up £4m a year for his five-year deal at City, the PFA will get £1.25m.
One agent said: "It's an absolute joke but I can see the irony here. Agents used to complain the PFA's fees were so low.
"As a consequence, the PFA now charge five per cent of every deal."
Boss Arsene Wenger remains on the trail of Fulham's Aussie ace Schwarzer, 37, with a £2million offer on the table.
Given, 34, would jump at a move to the Emirates - having been displaced by Joe Hart at City.
But Wenger says there are huge difficulties in trying to sign Given, not least financial.
Wenger said: "You can't offload the players when the financial difference between the two clubs is too big as no one can pay the wages.
"I don't know how much their keepers get each year but you must pay the players who go.
"Anyway, City need two keepers. They offered Shay Given a new deal."
Wenger insists Arsenal's conscience is clear in their pursuit of Schwarzer despite the fact it has been compared to Barcelona's courting of Cesc Fabregas.
He said: "If a club says 'no' you don't continue. We always behave like that."
Wenger laughed when told Blackpool boss Ian Holloway had called him a genius and replied: "He's the genius - not me. At the moment, he's higher in the table than Arsenal!"
The Welsh striker is too afraid to leave his house on the outskirts of his hometown for fear of being mobbed - and it can only get worse after his sensational goalscoring debut in Saturday's 4-0 crushing of Doncaster.
The on-loan Manchester City star said: "I can't describe how this feels.
"I grew up here and played and watched a lot of football in Cardiff. Playing for my hometown club is a dream come true. This will always be my home.
"But I've had a bit of a shock because my life has changed. This was the one place where I always felt I had a private life.
"I didn't have that in London, Manchester, Glasgow or anywhere else I've played but I had it here. Not this past week though."
Bellamy, 31, added: "I was more worried before this game than any other because impressing these fans means so much to me.
"They didn't let me down with their welcome and, hopefully, I gave them something back."
Manchester City boss Mancini made no secret of his admiration for Liverpool's super striker over the summer and hinted he would make a bid.
But the Merseysiders were determined to hang on to the £50million-rated star so Mancini had to look elsewhere.
And he believes the £22.5m he paid Inter Milan for Balotelli will prove to be much better value for money.
The two hitmen could go head-to-head tonight as big-spenders City host the Reds at Eastlands.
Mancini said: "Torres is a fantastic striker but I think it was difficult for Liverpool to sell him because he's such an important player for them.
"But it's good for us that we got Balotelli instead.
"Balotelli could be even better than Torres because Torres can only play as a striker. Balotelli can play as a striker or as a winger.
"What is sure is we are talking about two fantastic players."
Balotelli only celebrated his 20th birthday on August 12 but Mancini, who also worked with him at Inter, believes he is already one of the best in the world.
Mancini said: "In my view, there are eight or nine fantastic strikers in the world - and Torres and Balotelli are two of them.
"Then there's Ibrahimovic, Ronaldo, Tevez and Messi. They're all fantastic players and we've managed to get one of them."
Premier League sides know all about Torres, 26, who has been terrorising defenders in England for three years.
But Balotelli is a surprise package and his debut in the Europa League qualifier last Thursday suggested he will be real handful.
He scored the only goal against Romanians Timisoara but picked up a knee injury. Yet scans revealed no serious damage and he is expected to feature tonight.
Mancini added: "He is suited to the Premier League because it is different to Italy's Serie A. The defenders do not know much about him but they will see he can change everything about a game. It's the same with Carlos Tevez.
"I saw Mario four years ago when he was 16. It was the last five games of the Serie A championship.
"Zlatan Ibrahimovic was injured and we played Mario inside and he played like someone of 30 years old. That's because he has good technique - he has everything.
"Mario is young, always wants to play and always wants to score."
Mancini shares a common bond with his Kop opposite number Roy Hodgson as they have both managed Inter. And City's Italian chief reckons the Reds could be the surprise contenders for the Premier League title under the careful stewardship of Hodgson.
He said: "Roy is a good manager. I know him very well as he worked in Italy for many years. He is like me - and that is a good thing!
"Liverpool are a strong team and have only changed the manager - they have kept all the players they had last year. That means they can challenge for the title."
City keeper Joe Hart is ready to face Torres if the Spaniard is handed a first start the season by Hodgson. And while he rates the former Atletico Madrid star as world-class, he reckons City have players who fall into the same bracket.
England's new first-choice stopper said: "Torres had a difficult summer but you know for a fact that at any moment he can turn it on and score.
"You have to be aware of that with world-class players but we have a few ourselves.
"Liverpool will challenge for the title. Having a new manager changes a lot and a few people feel they have fresh chances and stuff to prove.
"But that's exactly how we feel at City so it should be an interesting game."
Manchester City's German defender, 21, cost £10.5million from Hamburg in June.
He hurt his left knee during Germany's 2-2 friendly draw with Denmark on August 11.
To make matters worse a stewardess rammed his damaged knee with her drinks cart on the flight back.
World Cup star Boateng, who is now being treated for a torn ligament, groaned: "This is annoying."
Fenerbahce and Besiktas have bid for the Manchester City star. But he said: "I'm not going to play there right now."
The Swede's relationship with Barca boss Pep Guardiola has been fractious since he joined the club from Inter Milan in 2009.
And the arrival of £35million man David Villa looks to have pushed him down the Nou Camp pecking order for the forthcoming Spanish season.
That has led Ibrahimovic's representative, Mino Raiola, to suggest his client could call time on his stay with the Catalans.
Raiola said: "Zlatan signed with FC Barcelona — not FC Guardiola. He signed him to play and then left him on the bench."
Ibrahimovic hit 23 goals in 46 games for Barca last season and is regarded as one of Europe's leading strikers.
But Raiola insists only three of the continent's biggest sides would be able to afford the Sweden international, who is rated in the £40m bracket.
He added: "There are only three clubs that are capable of signing Ibra — AC Milan, Manchester City and Real Madrid.
"These clubs are the only ones who can afford to sign him, to pay him and attract him.
"But Zlatan will be the one who decides whether he leaves and where he will go."
The Republic of Ireland keeper lost his place to Joe Hart.
But Given, 34, will return for the Europa League play-off second leg against Timisoara with City holding a 1-0 lead.
The Eastlands club are refusing to let Given go out on loan and would only sell him if they had a top quality replacement lined up to be the No 2.
That is not the case with just five days left before the transfer window closes.
So Given has been told to fight for his place with a transfer possible in the New Year, IF he has failed to dislodge Hart and wants to leave.
Boss Roberto Mancini said: "It would be important for Shay to stay.
"We need two good keepers but Shay must decide. I understand if he wants to leave but hope he will stay."
Manchester City came within three points of landing a place in Europe's top competition, just being edged out by Tottenham.
But Mancini insisted: "The Europa League is important - it's not like the Champions League but it's still important.
"Getting to the group stage was our first objective.
"It's a competition we want to do well in.
"It's difficult in the Europa League because you play more games.
"But if you can change some players every game you can arrive at the final."
Goals from Shaun Wright-Phillips and Dedryck Boyata saw off Romanian minnows FC Timisoara.
Mancini claimed his squad was big enough to see off the might of Juventus, Liverpool and Porto.
He said: "We have got a lot of good players - they can play in different positions and change without a problem."