Kenny Dalglish is being widely tipped to take charge of Liverpool until the end of the season with the club's owners believed to be ready to turn to an interim coach.
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A number of newspapers in England claimed on Saturday that NESV had started the search for Roy Hodgson's successor after the dismal performance in the 1-0 defeat to Wolves.
A last-gasp 2-1 victory over Bolton on Saturday - and the impressive second-half performance - should now buy Hodgson more time, but there is a view that the reprieve may not last long.
The Sunday Telegraph claims "Hodgson's persistent failure to elicit consistent results and performances from his team, as well as the breakdown of his relationship with the club's fans, has convinced Fenway Sports Group to bring forward their initial plan to review his position in the summer".
The view across Sunday's papers is that the owners, despite ideally seeking a permanent replacement, are now looking at Dalglish as a temporary option before making an appointment in the summer.
Speaking ahead of Saturday's victory over Bolton, Dalglish told the Liverpool Echo: "Let's just press the pause button and throw all our efforts and energies into one basket.
"Everyone - whether players, supporters, staff or whatever - has to throw everything towards the one aim and that is to get us three badly needed points from the game against Bolton today, because if everyone sticks together, we'll have a better chance of getting those three points.
"Then if we want to have a discussion after that, we can, but the three points for the club is more important than any single person and how they feel.
"So let's forget the issues today and concentrate on getting those three points."
Hodgson has made attempts to build bridges with the Liverpool fans in recent days and insists he retains the support of the players.
Asked in Saturday's post-match press conference whether he had the support of the owners, though, his answer was more equivocal.
"I guess so," he said. "It is not about me. I am very pleased and honoured to have this job.
"It is about Liverpool Football Club and performances so I don't take the speculation seriously of course. I shall probably have to learn to accept I shall get a lot of brickbats."