The 23-year-old was again in strong form for David Moyes's side during the 2021-22 campaign, making 48 appearances in all competitions, contributing four goals and four assists in the process.
However, according to football.london, West Ham have again reiterated that the England international will not be allowed to leave the club under any circumstances this summer.
West Ham have Rice on a deal until June 2024, with the option of a further 12 months, but he has allegedly recently rejected the chance to sign an extension at London Stadium.
The Hammers are said to value the midfielder in excess of £150m and do not believe that any team in world football would be prepared to pay that amount for him in the current market.
Rice has scored nine times and registered nine assists in 192 appearances for the Hammers in all competitions, and he again excelled for the London club during the 2021-22 campaign.
The midfielder played an important role in Moyes's side reaching the semi-finals of last season's Europa League, scoring three times in 10 appearances, while he scored once and provided four assists in 34 Premier League appearances, as the capital outfit claimed seventh position.
Chelsea are believed to have made a fresh approach for Rice in recent days but were told that he would not be allowed to leave in the current market.
West Ham recently allegedly offered Rice an eight-year contract worth £200,000 a week, but the deal was rejected, as the Englishman wants to be playing regularly in the Champions League at this stage of his career.
The midfielder does not need to leave his current club for international reasons, as he is already a key player for the Three Lions, but he is said to be determined to challenge for major trophies in the near future.
"The first thing to say is that he is not for sale. If you are interested, well, it will be north of that. £100m was cheap last summer. £150m just now would be the minimum but he is not for sale," Moyes said when questioned on Rice in April.
"What I do know is that it means there are only certain clubs that could even consider it."
Real Madrid are thought to view Rice as a possible alternative to Borussia Dortmund's Jude Bellingham, with Los Blancos potentially being priced out of a move for the former Birmingham City youngster. body check tags ::