It has been reported that the Blues want to sign a defensive midfielder for next season and beyond and have identified Rice as a potential candidate.
Chelsea released the 21-year-old - who can also operate as a central defender - as a youth player, but the London club have been impressed with how the England International has progressed at the Hammers, according to the report.
Rice has made 29 appearances in the Premier League for West Ham so far this season, while during the 2018-19 campaign, the youngster scored two goals in 34 league matches for the London club.
Football in England is suspended at the moment due to the coronavirus pandemic.
When the campaign eventually gets back underway, West Ham will be hoping to stave off relegation to the Championship.
David Moyes’s side are 16th in the Premier League table at the moment with 27 points from 29 matches, level on points with third-from-bottom Bournemouth.
Meanwhile, Chelsea currently find themselves fourth in the standings with 48 points from 29 matches.