The Blues are committed to a significant overhaul of their squad this summer as they pursue deals for Bayer Leverkusen's Kai Havertz and Leicester City's Ben Chilwell having already signed Hakim Ziyech from Ajax and Timo Werner from RB Leipzig.
Head coach Frank Lampard is prioritising other areas of the team aside from centre-back but now recognises a need to strengthen in that area given Chelsea's poor defensive record this season.
Rice is predominantly playing as a holding midfielder for the Hammers but Lampard is keen on reverting the 21-year-old to the central defensive position he occupied earlier in his career, given his ability on the ball would enable him to play out from the back effectively.
However, West Ham believe they are in a strong position to repel any interest as Rice is contracted to the club until 2024 -- with an option for a further year -- and the England international is said to be happy and settled in east London.
Lampard knew Rice as a youngster when he spent time at the Chelsea academy while midfielder Mason Mount is a close friend but the Hammers are hopeful they can hang onto their prized asset.
Relegation would inevitably force a rethink on all sides but West Ham's victory over Chelsea last week helped them move four points clear of the relegation zone with five games left.
Manager David Moyes has publicly stated he wants to keep Rice and the club are hopeful a price tag in excess of £70 million would be enough to ward off interest from Chelsea and also Manchester United, who have been monitoring his situation.
Financial pressures from dropping to the Championship would make it harder for the Hammers to keep Rice this summer but it is understood the club are keen to avoid cashing in on key players in any event and are exploring other ways to ease any monetary concerns.