Cristiano Ronaldo and Gary Neville, who both missed Saturday's win over Wigan, are racing to be fit for United's Champions League match against Copenhagen on Tuesday.
Ronaldo is recovering from an ankle injury sustained on international duty with Portugal, while skipper Neville (calf) trained on Monday and is rated as a possibility for the match.
"Cristiano Ronaldo hopefully should be OK and Gary Neville is a possibility," Sir Alex said at United's pre-match press conference. "We're not 100 per cent certain Ronaldo will be fit for Tuesday, but he has improved from the weekend.
"He's put a lot of work into his rehabilitation. He spent five hours in the swimming pool working on the flexibility of his ankle, so he's making a big effort to be there."
Even if the Portuguese winger does not win his race for fitness, Sir Alex has no qualms that Darren Fletcher, also back from injury, or Ole Gunnar Solskjaer, who played on the right against Wigan, can offer something different from the right flank.
"After Ole's performance on Saturday, I'd be happy to stick with him," he said. "I also have Darren Fletcher who can play there, and he's had a fantastic season."
United defenders Gabriel Heinze (hamstring) and Mikael Silvestre (foot) are both still out, although Gaby is in training this week and could play against Liverpool on Sunday. "Gaby won't make Tuesday's match," he added. "He's possibly looking at the Liverpool game. He did much better in training on Monday, but he's definitely out of the Copenhagen match."
The return of Ronaldo and Neville is important as Sir Alex hopes his team can record back-to-back wins over the Danes in order to guarantee United's place in the knockout phase.
"If we win our next two games home and away against Copenhagen, we'll be in a great position," he said. "But you have to repsect teams. We will do that. Having watched videos of Copenhagen's two games against Benfica and Celtic, we know they have good qualities. It won't be easy but our form is good and we have a real goal threat about us. In the second half against Wigan we could have scored a few more goals.
"Going into a European game I couldn't really ask for any more. I'd like every player in the club to be fit but that doesn't happen in modern football. We've had to deal with injuries, but I think we'll have a side strong enough to win the match."
Copenhagen only have a point so far in the group, adding to Sir Alex's belief that the Danish side will come to Old Trafford and go for the win. He said: "They are in the weakest position. The result at Celtic Park wasnÂ’t a good one for them. They really needed something from that match.
"But, one result can change everything. ThatÂ’s why I think Copenhagen will try to win the match, which would be refreshing in terms of football today. They are strong defensively and are powerful in the air. They are a decent team and I will not be dismissing them at all. They could qualify, but they need to start winning."