While Rice is regarded as the biggest asset at the Hammers, there is an inevitably about a future move to a bigger club.
Chelsea have been heavily linked with a move for the England international, who was a boyhood Blues fan and has previously spent time in their youth ranks.
However, according to Football Insider, United are prepared to pay big money for the 21-year-old.
Although United are well stocked for options in central midfield, Ole Gunnar Solskjaer may look to use Rice in the middle of his defence.
Rice still has four years remaining on his contract, leaving West Ham in a strong position regarding the academy graduate's future.