The west Londoners are long-term admirers of the England international, who is said to have impressed Blues boss Frank Lampard on several occasions last season.
Despite their major spending spree this summer - which has seen them splash out close to £230million - Chelsea are said to be willing to fork out £80million to acquire Rice's services.
And according to Italian journalist Nicolo Schira , last season's beaten FA Cup finalists are closing in on the 21-year-old after agreeing a five-year contract with him.
He tweeted: "Chelsea are literally on fire: after Mendy’s signing, Blues are working to close Declan Rice’s deal.
"Talks ongoing with West Ham (rejected a bid of €50M + add-ons). The midfielder has already agreed personal terms for a 5-year contract."
Chelsea will face stern opposition from the West Ham brass to bring Rice back to Stamford Bridge as the Hammers are hell-bent on keeping him at the London Stadium.
West Ham co-chairman David Gold appeared to reiterate the club's stance on selling Rice earlier this month after he made his 100th league appearance for the club in their opening day defeat to Newcastle.
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He tweeted: "I would like to congratulate Declan on his 100th Premier League appearance for West Ham United - a magnificent achievement.
"I am very proud of him and he epitomises everything that this great football club stands for."
But talkSPORT's Adrian Durham reckons Gold and David Sullivan should seriously considering cashing on Rice and using some of the funds to sign Burnley defender James Tarkowski.
“The thing is Declan Rice is a good player – I do like him," Durham said of the former Chelsea academy star. “Maybe some people think he’s better than what he actually is, but I do like him.
“I do think he’s an England standard player and he is one of West Ham’s better players – you could argue that he’s their best player.
“But is he a match-winner on his own? Can they do without him? And I think the answer to that is yes.
“And if they do get a lot of money in for him and they do spend it wisely on the players [David] Moyes thinks will make West Ham’s first team better than I think that it’s got to be a consideration.
“The story was last week is that they wanted [James] Tarkowski and they could get him for what £50m? That’s what Burnley were talking about. They could maybe get him for a little bit less than that.
"If you sell Declan Rice and you sell Tarkowski then you’ve got some money left over then I think that’s got to represent a positive deal for West Ham United.”