The Englishman is someone former Blues boss Frank Lampard wanted to sign for the defensive midfield spot.
However, Lampard is out at the club and Thomas Tuchel is now in charge.
According to The Guardian, it was Lampard who was the 'main driver' behind pursing Rice, not the club's board.
West Ham are determined to keep the 22-year-old and have slapped an £80m to deter any suitors.
One of which could be Liverpool, who are eyeing a summer move for Rice as they look to replenish their squad.