The 24-year-old is tied down at the club until 2024 and is unlikely to extend his stay - despite being offered an eight-year contract by the Hammers last year.
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Rice publicly spoke of his desire to play Champions League football in December during the World Cup, while outlining his ambition to win 'big trophies'.
And the Hammers know they may have to cash in on the player - who Kieran Trippier has claimed is better than Thomas Partey and Casemiro - in the summer to avoid losing him on a free transfer.
talkSPORT understands he may cost a whopping £120million, with boss David Moyes recently stating he will only leave for a British record fee.
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West Ham sporting director Mark Noble has insisted he will not begrudge his ex-teammate from departing with the club to not stand in his way of a move.
But it's not just Graham Potter's side that are interested, as talkSPORT takes a look at Europe's elite clubs vying for his signature.
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Chelsea
Rice has long been linked with a return to Chelsea after he was let go by the club in 2014.
Known to be close friends with Blues playmaker Mason Mount, Rice declared in 2020 how he would love to play alongside his compatriot at club level.
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The Hammers skipper has also gotten the seal of approval from Chelsea's record signing Enzo Fernandez, who admitted he studies Rice's game to help him improve as a player.
Chelsea are believed to be in the market for a new defensive midfielder with N'Golo Kante facing an uncertain future with the Frenchman poised to become a free agent.
Meanwhile, Denis Zakaria is set to return to Juventus when his loan spell ends, and with Jorginho sold to Arsenal in January, Chelsea know they have to add to their squad depth.
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Arsenal
The Gunners are believed to be leading the pack in the race to secure Rice's services, with Mikel Arteta identifying him as his no.1 target.
talkSPORT understands Rice is 'favouring a move' to the Emirates with the north Londoners primed to return to the Champions League for the first time since the 2016/17 season.
Analyst Danny Murphy believes Rice would be a 'perfect' fit for Arsenal where he would be used in a rotational system alongside Thomas Partey and Granit Xhaka.
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Arsenal have improved drastically this campaign following last year's fifth-placed finish, and look as though they could once again compete for top honours in the future.
Manchester United
The Red Devils are long-term admirers of the combative midfielder, with talkSPORT host and ex-Crystal Palace chairman Simon Jordan stating his future lies at Old Trafford if United continue to improve.
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United could have the money to sign him in the summer as Qatari investors weigh up buying the club for £6billion.
Should the takeover materialise, United are expected to make high-profile marquee signings, which could seem them press ahead with a move for Rice.
talkSPORT's Jim White revealed earlier this week how United had a £100m offer rejected by West Ham last summer.
And it wouldn't come as a shock if they reignite their interest in Rice where he would partner Casemiro in the middle of the pitch.
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Manchester City
United's rivals City are also claimed to have Rice on their radar as they aim to bolster their midfield in the summer.
According to The Times, Rice - along with England teammate Jude Bellingham - have been identified as potential options for the Citizens.
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Ilkay Gundogan has entered the final six months of his contract, while Bernardo Silva is open to a new adventure away from the Etihad.
However, any move for Rice could be derailed by the threat of sanctions from the Premier League after City were charged with more than 100 alleged breaches dating back to the 2009/10 season.
If found guilty, City could be slapped with a huge fine, a points deduction or even expulsion from the top-flight.
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Liverpool
Another club in dire need of a new midfielder, Liverpool trio Naby Keita, James Milner and Alex Oxlade-Chamberlain are all set to depart as free agents.
Meanwhile, Brazil international Arthur Melo will be going back to Juventus after his disastrous loan spell.
And Fabinho and Thiago Alcantara have struggled for form this campaign to further the need for fresh blood in the middle of the pitch.
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Like City, Liverpool are also keen on Bellingham, though Italian reporter Rudy Galetti has stated that they are also keeping tabs on Rice.
He told CaughtOffside: "It's too early to talk about negotiation between clubs because West Ham don't want to discuss about Rice with any clubs until June.
"But for sure, Arsenal will be one that will follow the player with great attention during the next transfer window, and in that sense, we also need to pay attention to Liverpool, who are really interested in him."
However, with Liverpool languishing in tenth spot, it seems unlikely they will secure Champions League football to persuade Rice to join.
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Newcastle
The Magpies have emerged as a shock destination following their stunning season with Eddie Howe's men on course to finish in the top four.
With the Toon outfit performing way above expectations, their Saudi owners could look to splash the cash in the summer to cement themselves as a regular 'top four' side.
CBS Sports journalist Ben Jacobs has insisted a move for Rice cannot be ruled out, though he acknowledged that Arsenal remain the favourites.
He said: "Arsenal's midfield priority will be Declan Rice and West Ham are resigned to losing him.
"Chelsea also really want Rice. Manchester United and Newcastle United can't be ruled out either, although I understand Rice's preference is to stay in London.
"That won't be a deal-breaker, but Arsenal and Chelsea can certainly use it to their advantage. Rice also wants Champions League football.
"Rice has also spoken glowingly about Arteta. So it's probably fair to term Arsenal the favourites right now."
Real Madrid
The LaLiga giants are said to have identified Rice as a potential signing with Luka Modric and Toni Kroos in the twilight of their careers.
Spanish news outlet Defensa Central revealed last year how Rice's name had been mentioned several times by board members at the Bernabeu.
They insisted that Los Blancos were keeping an eye on Rice's situation at West Ham ahead of a possible transfer this summer.
But it appears they have since ruled themselves out of the running with Rice 'giving his word' to Arsenal that he will link up with them.
That is according to El Nacional, who have reported that Real president Florentino Perez has accepted defeat in his pursuit of the player.
West Ham vs Chelsea is live and exclusive on talkSPORT on Saturday 11 February at 12:30pm