According to Sky Sports journalist Florian Plettenberg, there's a good chance that the midfielder will move on this summer with his contract set to expire in 2024.
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However, the Blues won't have things all their own way with Arsenal and Manchester United also linked with a move for the player.
The Gunners are believed to be favourites to complete a deal, with their pursuit of the Premier League title putting them in a very strong position to make the move possible.
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But Chelsea will be hoping that they have an advantage in bringing the player back to west London given that Rice advanced through the youth academy at Stamford Bridge before heading to West Ham.
The England star has been regularly linked with a move away from east London due to his fine form in recent season.
Now 24 years of age, Rice has made 229 appearances for West Ham, scoring 12 goals in the process.
A leader on the field, Rice officially replaced Mark Noble as club captain last summer following the veteran's retirement from the game.
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The midfielder is also a regular starter for England, winning 39 caps already and establishing himself as a core player for Gareth Southgate.
It remains to be seen what the future holds for Rice, however his immediate focus will be on ensuring that West Ham avoid being dragged into a relegation battle with the club currently 17th in the table and out of the drop zone on goal difference.