Blues boss Frank Lampard is an admirer of Rice and the Stamford Bridge outfit have been linked with wanting to sign him this summer.
It has been claimed Chelsea have made a move for Rice and put in a £50m bid, but West Ham have dismissed those claims.
The Hammers insist that a £50m bid would be laughed off and are hoping that Rice remains at the London Stadium for many years to come.
Rice is under contract with West Ham until the summer of 2024 and the club boast an option in his deal which would extend that by a further year.
The ball appears to be in Chelsea’s court to slap in an offer which West Ham cannot refuse if they want to land Rice this summer.
Rice played in all West Ham’s 38 league games this season as the Hammers successfully avoided relegation from the Premier League.
The midfielder, who can also operate in defence, has now made a total of 109 appearances for West Ham.”