The England international's future remains the subject of much speculation, with Manchester United believed to be interested in bringing him to Old Trafford during this summer's transfer window.
Meanwhile, Chelsea are also allegedly keen to bring their former youngster back to Stamford Bridge providing that they are able to address their ownership issues in the near future.
West Ham are believed to have set a £150m asking price for a player who still has two years left to run on his current deal, with the option of an additional 12 months.
A recent report claimed that the Hammers had offered Rice an eight-year contract worth £200,000 a week in a bid to convince him to commit his future to the club.
However, according to The Sun, the England international will reject the opportunity to pen the lucrative deal, as he does not want to be committed to the club for such a long period of time.
Harry Kane failed to force a move away from Tottenham Hotspur last summer due to the length of time on his contract, and the report claims that Rice is wary of being caught in a similar situation.
The midfielder's next move will allegedly not be driven by wages, rather the opportunity to win major trophies, while he wants to be playing in the Champions League on a yearly basis.
Rice has again been in strong form for West Ham during the 2021-22 campaign, scoring five times and registering four assists in 48 appearances in all competitions.
The 20-time English champions will allegedly have around £100m to spend on new players this summer, with the club's finances being impacted by their failure to qualify for next season's Champions League.
Man United are currently battling West Ham for sixth position in the Premier League table, which would bring a Europa League position for next season.
Meanwhile, Chelsea's plans for the summer window have been placed on hold, with the club currently unable to bring in new players due to their off-the-field issues. body check tags ::