The 23-year-old midfielder has been strongly linked with a move away from the London Stadium amid interest from the likes of Chelsea, Manchester United, Manchester City and Real Madrid.
Chelsea are understood to have had a fresh approach for the England international rebuffed by the Hammers earlier in this summer's transfer window, with David Moyes's side insisting that he is not for sale.
While Rice looks set to stay at West Ham this season, his long-term future is still believed to be uncertain as he will have just 12 months remaining on his contract in the summer of 2023.
According to talkSPORT's Alex Crook, Rice has a 'gentleman's agreement' with West Ham to stay for the 2022-23 campaign but the midfielder is likely to leave the club next summer.
Crook also claims that Chelsea will be the frontrunners for his signature if the Blues qualify for the Champions League.
Rice, who is allegedly valued at £150m by West Ham, has made 192 appearances in all competitions for the Hammers and is set to become the permanent captain next season following Mark Noble's retirement.
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