The England midfielder has been chased by Manchester United and Chelsea, but both clubs have been reluctant to pay the mammoth fee for the 22-year-old.
According to The Telegraph, Rice, who was released from Chelsea's academy aged 14, is unhappy he has effectively been priced out of a move away and currently has no plans to pen a new deal in east London.
Rice has established himself as one of the best holding midfielders in the Premier League since breaking through for the Hammers three years ago but only has two years left on his contract after turning down new terms on two occasions.
However, earlier this week former Crystal Palace owner Simon Jordan laughed off West Ham's reported price tag for Rice.
"Let's be clear about this nonsense you keep trotting out about David Moyes telling us he's got a £100m player," the former Palace owner told co-host Jim White.
"He hasn't got a £100m player, because if he had a £100m player someone would be bidding 100m quid for him and they'd be selling him.
"If West Ham are the only people in the room regarding him as a £100m player and nobody else does then he isn't a £100m player, is he?
"Michael Carrick was pivotal to a successful Manchester United team at times, but he wouldn't have gone for £70m or £60m quid like some other players were because you look at players in different ways, don't you?"
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