Frank Lampard is a known admirer of Rice, 21, and wants Chelsea to bring him to Stamford Bridge before the summer window slams shut next week.
The Blues have already spent more than £200million this summer on the likes of Timo Werner, Kai Havertz, Ben Chilwell and Edouard Mendy but Lampard wants the club to force through one more deal as he looks to challenge for titles in his second season in charge.
However, West Ham are reluctant to lose Rice, who has developed into one of their most consistent players over the past four seasons, and value the player at around £75m.
That figure will likely be beyond Chelsea given their summer spending to date but the club are hoping to tempt West Ham to agree to a cheaper deal by offering two players as bait.
The Transfer Window Podcast say Chelsea have offered Germany defender Antonio Rudiger and England midfielder Ruben Loftus-Cheek to the Hammers as they attempt to secure a deal for Rice.
Rudiger has made more than 100 appearances for Chelsea since joining the club from Roma in 2017 but has fallen down the pecking order following the arrival of Brazilian legend Thiago Silva.
The 27-year-old is yet to feature for Lampard’s side this season and been linked with a number of clubs, including Chelsea’s London rivals Tottenham.
Loftus-Cheek, meanwhile, is also struggling for game-time at Stamford Bridge and Lampard admits he could be set to leave on loan.
‘I am very open with Ruben. We have had a couple of conversations in the last week,’ Lampard said earlier in the week.
‘He is fit as a fiddle so he could play week in, week out, but he needs to play.
‘But if it’s not the right option, he will be competitive in this squad as well because of the qualities he has and hopefully be a big plus for us, so I am relaxed about it.’
Rice helped West Ham avoid relegation last season and has played every minute of their three Premier League fixtures so far this term.
Speaking after West Ham’s emphatic victory over Wolves on Sunday, Hammers coach Alan Irvine said Rice was ‘extremely happy’ at the club.
‘He was captain today [against Wolves], he is not somebody with other things on his mind,’ Irvine said.
‘All the players and staff have been fantastic. Declan is extremely happy here and is an important player for us.’