The 62-year-old, who joined the London club in 2007 and guided them to the Europa League final last season, is even being tipped to fail at Anfield by some players at Craven Cottage.
Others claim that, although Hodgson is widely respected in the game, his brand of management and style of football will have to change radically if he is going to succeed at Liverpool.
“I’m not entirely sure this is the right move for Roy,” one senior player at Fulham told the Sunday Mirror. “He’s a lovely bloke and I wish him all the success in the world but I suspect he might have taken on more than he can handle going to Liverpool.
“He loathes confrontation and can’t handle egos and troublesome personalities.
“He certainly bit off more than he could chew with Jimmy Bullard at Fulham, so can you imagine him dealing with players at Liverpool like Steven Gerrard, Jamie Carragher and Fernando Torres who have enormous power in and out the dressing room?
“He can also be rigid and inflexible as well. Certain players hit a bad run of form at Fulham but Roy refused to make changes even though their performances on the field were deteriorating.”
Another player said: “Roy likes to surround himself with a certain type of player. Foreign players are less likely to come and smash down the manager’s door complaining about not playing.
“He doesn’t want troublemakers at the club, he wants players who are happy to sit patiently biding their time waiting to play.
“If there are problems he will promise you the world, fail to deliver but leave his coaching staff to deal with the fall-out.
“Personally, I think he has made a big mistake going to Liverpool.
“Steve McClaren is a good example of what can happen when you step out of your comfort zone. Didn’t he lead Middlesbrough to a major European final? Look what happened to him when he left and took over England. It’s a big gamble.”