Rice has been a key figure for West Ham since breaking into the Irons’ first team and his form has been rewarded by Gareth Southgate at international level.
Frank Lampard is desperate to shore up his defence which has cost Chelsea on several occasions this season.
Now he could be set to turn to the 21-year-old to solve his woes at the back.
According to Football Insider, Chelsea are prepared to offer one or more of Fikayo Tomori, Kurt Zouma and Michy Batshuayi to seal a deal for Rice.
Tomori was with Lampard at Derby last season but has fallen out of favour in the second half of the campaign despite a promising start to his senior career in west London.
Kurt Zouma was behind Antonio Rudiger and Andreas Christensen in the pecking order before being given a chance to impress.
He did just that against Crystal Palace but was off the pace in the 3-0 defeat to Sheffield United.
Batshuayi is a player that has been of interest to West Ham in the past.
David Moyes will be looking to add some extra firepower to his side if they beat the drop.
The writing was on the wall for Batshuayi at Chelsea during the break when he was left out of an inter-squad clash before the restart.
Former Chelsea striker Chris Sutton believes the Blues also need to replace Kepa Arrizabalaga if they’re to seriously challenge next season.
“What’s been the positives for Chelsea this season?” Sutton told Stadium Astro.
Chelsea could offer Tomori, Zouma and Batshuayi as part of the deal
“The likes of [Mason] Mount coming to the fore, Tammy Abraham coming to the fore, they’ve now done some good business with [Hakim] Ziyech and [Timo] Werner, so things are looking up.
“But they need to do some more business as well.
“I think the goalkeeper is a massive issue and defensively they’ve conceded two many goals.
“Frank will know that but there’s no point worrying about that at this moment in time.
“Get over the line, get a Champions League spot, you know the riches which come from the Champions League and the finance which comes with that, and then he can address all these issues once the season finishes.”