Rice was heavily linked with a move to Chelsea during the summer transfer window, but the Hammers were reluctant to let him go.
Frank Lampard reportedly is a big admirer of Rice, and it would take a fee in the region of £80 million to lure him away from the London Stadium.
According to a recent report from The Mirror, Rice has informed his friends that he would prefer to stay in London and has no interest in joining Manchester United, another club who are interested in signing him.
Rice is enjoying a superb campaign once again, and West Ham are in no rush to sell him in the next summer.
SL View: Do Liverpool need him?
The midfield is one area where Liverpool may look to bolster in the summer.
Gini Wijnaldum has refused to sign a new contract extension at the Anfield club, and the Dutchman could leave for nothing.
The 22-year-old is a defensive midfielder, and like Fabinho can drop in defence if needed. Liverpool can use his versatility as they look to bolster their defence as well.
It is evident this season that new faces will have to arrive at Anfield to continue the progress under Jurgen Klopp, and Rice would be a fantastic addition.
Chelsea still remain big favourites, but Rice could be tempted to join the Reds where he has a better chance of winning trophies and play under a world-class manager who can take his game to the next level.