The Scot, appointed two weeks ago to lead the search for a new manager, has informed the board their preferred candidate does not have his support.
Dalglish, a popular figure among Liverpool’s supporters for his achievements as player and manager, has made it clear that he believes he is the contender most suited to steering the club through the most turbulent period in its history.
But despite that recommendation and reports of talks being held with Manuel Pellegrini, the former Real Madrid manager, Hodgson remains favourite to be handed the post, with some sources suggesting his appointment will be ratified in the next 10 days.
Should that come to fruition, Dalglish is likely to find the position he currently occupies at the club untenable. He had returned to Merseyside last year with responsibility for Liverpool’s Kirkby Academy - a role in which he has enjoyed significant success, helping to secure the signatures of two of England’s most promising youngsters - as well as his more public ambassadorial duties.
Hodgson, who guided Fulham to an unlikely appearance in the Europe League this year, has been identified by Liverpool’s hierarchy as the safe pair of hands required to restore calm to Anfield after a chaotic spell as Benítez’s tenure came to an end.
His possible arrival has not been unanimously welcomed in Liverpool’s dressing room, with a number of players believed to be concerned by the lack of silverware on an otherwise impressive CV.
His appointment would by no means prompt an exodus - Daniel Agger this week joined Pepe Reina in voicing his loyalty to the club regardless of who succeeds Benítez - but the board’s belief that Hodgson would unite the players appears misplaced.