The 22-year-old excelled for the Hammers last term and also played a key role in England's progression to the final of this summer's European Championship.
Rice's performances at the start of the new season have also been of a high standard, and he scored his first goal of the campaign against Dinamo Zagreb in the Europa League on Thursday night.
Man United were linked with the midfielder over the summer, but West Ham have him on a contract until June 2024 and are believed to value the former Chelsea youngster in excess of £100m.
Rice, who has captained the Hammers in all four of their Premier League matches this season, is also believed to be admired by both Chelsea and Manchester City.
The defensive midfielder has scored six times and resisted six assists in 150 appearances for West Ham in all competitions since making his debut in 2015.