The 22-year-old has been an ever-present for David Moyes’ side in the Premier League this season, helping the Hammers in a surprise run to fourth place.
Rice’s form and potential has seen him linked with United and Chelsea, but TalkSport reports that the Hammers will stand firm when it comes to negotiations over a price.
Host Jim White revealed that he spoke with Hammers vice-chairman David Sullivan about potential summer bids.
“Sullivan has already told me it’s got to be north of £100m or they won’t entertain it,” White said
“We’ll wait and see what happens with that.”
If Moyes can achieve a remarkable top four finish for the east London club, Rice’s chances of staying will undoubtedly improve with the promise of Champions League football.
The Hammers are currently fourth, two points ahead of Chelsea in fifth, with 13 rounds of the season left to play.
Rice has played every minute of their league campaign so far, scoring one goal in 25 appearances.
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