The West Ham star is top of Frank Lampard’s wish list, who tried to sign him in the summer window.
Ultimately, a transfer failed as the Blues could not move on the likes of Antonio Rudiger, Marcos Alonso and Jorginho to raise funds.
The Hammers also told Chelsea that Rice was not for sale.
But their resolve is set to be tested further in January with some of the biggest clubs in the Premier League interested.
According to Todofichajes, United, City and Liverpool are all interested in the England international, as well as Chelsea.
All four have contacted West Ham over a transfer but the London outfit are still looking to battle back any bids.
Ole Gunnar Solskjaer is a known fan of the midfielder but a summer deal could be more likely.
Despite the arrival of Rodri, Pep Guardiola has found his midfield overrun on occasion this season – especially on the counter – and Rice would negate that.
Liverpool have had the same problem at times, and the 21-year-old’s versatility is also a huge asset.
Chelsea are the most interested in Rice’s services, however, and remain favourites as the club he grew up with before being released at the age of 14.
But Todofichajes further report that West Ham are looking to tie him down to a new contract that would see him extend his stay in east London until 2026.
Failing that, the Hammers would be able to command a hefty fee – especially with growing interest in him.
Lampard is a huge fan of Rice and former Chelsea star Tony Cascarino has told the Blues boss what to expect from him if he does snap him up.
“Declan Rice can protect people,” he said.
“I learnt this early on in my career, one of the biggest skills you can have is do the simple things really well and if you can, you’ll be one hell of a player.”
As well as Rice, Chelsea have been linked with a move for AC Milan goalkeeper Gianluigi Donnarumma and Bayern Munich star David Alaba.
Both will be out of the contract at the end of the season and their futures are up in the air.
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