The 24-year-old has participated in all 24 Premier League games this season and has contributed two goals and two assists. His current contract with the club ends in June 2024, but the Hammers can extend it for an additional year.
Nevertheless, the England international is expected to depart from the London Stadium at the conclusion of the season because he has expressed his wish to join a Champions League team.
Several clubs, including Arsenal have reportedly shown interest in the midfielder and have contacted his representatives. However, according to TEAMTalk, Manchester City are the favourites to acquire the player.
The report suggests that the Premier League champions are ready to bolster their midfield as there is uncertainty surrounding the futures of Kalvin Phillips, Ilkay Gundogan, and Bernardo Silva.
It is believed that West Ham United would demand a fee of at least £100m for Rice.