They are also hoping to stump up another £20m for Rennes goalkeeper Edouard Mendy.
But according to reporter Simon Phillips, the Blues are eyeing one more major deal before the window closes on October 5.
That gives Frank Lampard just two-and-a-half weeks to get Rice through the door at Stamford Bridge.
Lamps sees 21-year-old midfielder Rice — who also plays in defence — as the ideal man to help the club get back in the Premier League title mix.
West Ham rate him at £80m and will do everything in their power to keep their academy graduate, who was released by Chelsea aged 14.
Chelsea, however, are determined to push the fee well down from the Hammers' asking price.