The People says the England international has told friends he wants to hook up with former international boss Sven Goran Eriksson at Manchester City in the summer.
He said he will make a decision over the summer, but privately has admitted it may be time to move on.
He is looking at European legislation that allows players to buy themselves out of five-year contracts when there is only two years left.
Crouch has found himself a bit part player this season as record signing Fernando Torres has smashed 24 goals since arriving on Merseyside.
A friend of Crouch said: "Peter has kept his mouth shut and tried to prove himself on the training ground every day but it obviously isn't enough.
"He knows if Rafa leaves in the summer then the new man might give him a fair crack but if Rafa stays then he will definitely move on.
"Manchester City are a team on the up and Peter knows they have a good chance of breaking into Europe next year and he won't have to move house either."