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Both Chelsea and Manchester United, however, could be put off by the eye-watering £100m price tag on Rice, which is slightly more than the Blues paid for Belgian powerhouse Romelu Lukaku.
The Telegraph's report also claims that Rice believes West Ham are now pricing him out of a move to bigger and better things, such as challenging for silverware and playing Champions League football.
But with just under three years remaining of his current deal at the London Stadium, any potential suitors will have to stump up West Ham's mammoth asking price to land the midfield maestro.
Despite the interest Rice has received, no offers have landed on the table of West Ham, with the high asking price an obvious factor.
West Ham's intention was not to price him out of a move, as they believe £100m is a realistic asking price.
It comes after last season, Hammers boss David Moyes suggested that the 22-year-old was worth "far more" than £100m.
“We’ve got some players that we value at £100million and we won’t be selling them,” Moyes told talkSPORT.
"I look at the players who have joined some clubs from overseas and come in and nowhere near had the impact Declan Rice would have.
"| don't agree with the owners that Declan Rice is a £100m footballer. Far, far more than 100m. Far, far more."