Chelsea have already had a very active summer, signing the likes of Timo Werner, Kai Havertz and Ben Chilwell, while they are also close to sealing a deal for Rennes goalkeeper Edouard Mendy.
However, Lampard still wants to bring in one last player before the transfer window shuts and has identified Rice as the final piece of his puzzle.
The Chelsea boss believes Rice can be reverted back into a centre-back and marshal a Blues back-line that conceded 54 times last season – as many as 15th placed Brighton.
However, according to The Athletic’s David Ornstein, not everyone shares Lampard’s view and there are significant reservations over the deal from a number of people in Chelsea’s hierarchy.
The biggest issue is the price West Ham will demand, which will be in excess of £70million – a fee the Blues are unlikely to be able to match without including players in a swap.
Interestingly, some at the club are not convinced he has actually addressed the ‘technical deficiencies’ that prompted that decision to let him go and are not in favour of the signing as a result.
While Chelsea may be split over whether Rice is the solution to their defensive woes, Lampard is in no doubt over his quality and believes he can become a world-class centre-back as well as offering cover in the defensive midfielder role.
Having spent so little this summer, though, and enraging even their own players with the sale of Grady Diangana, West Ham’s board are extremely unlikely to sanction the sale of the club’s best player, who was named Hammer of the Year last season.