Kevin Keegan, John Barnes and Steve McManaman insist Hodgson is not to blame for the club's alarming slide, which could see the Reds boss axed just six months after taking charge. That was looking increasingly likely, amid reports owners NESV had discussed whether to end the 63-year-old's reign.
"I don't think anybody wants changes of managers now because it just upsets everything," said McManaman. "That's more speculation, and it's in the middle of a very busy transfer window, which is difficult."
Such an outcome would please some supporters, who have long campaigned for the return of club legend Dalglish - a former player and manager and current academy ambassador.
But all the suggestions from NESV so far make that return to the past seem unlikely, as it has been hinted they would prefer a younger, more progressive man in charge.
Barnes, who played under Dalglish in the last Liverpool side to be crowned English champions, does not believe the Scot - or anybody - can wave a magic wand to transform the club's dwindling fortunes.
"Kenny isn't going to come and win the league because they still need a massive investment to improve the squad," said the former England midfielder. "If that happens, I'm sure Kenny would do a great job."
Barnes described Dalglish as the best manager he played under at Anfield.
"Kenny was the best but, fortunately for him, he also managed the best team," he said. "When he left, the team disintegrated and we didn't actually win the league. But I had my most successful period under Kenny."
Dalglish brought the young McManaman to Liverpool. "He was a fantastic manager," said the latter. "But that was 1989-1990 - that was a long, long time ago, and he's done many, many other things since then."