Speculation linking the England international with a potential switch to Old Trafford has quietened in recent months with United thought to be prioritising a summer move for Aston Villa's Jack Grealish.
However, according to the Daily Mail, the 20-time English champions are still considering the possibility of a move for Rice during this summer's transfer window.
The 21-year-old, who signed a new long-term contract with the Hammers in December, has made 26 appearances for his London club during the 2019-20 campaign.
The midfielder has not missed a single minute of his team's current Premier League season, meanwhile, and captained the side against Leicester City at the end of December.
Rice has also been capped on seven occasions by England and is expected to be in Gareth Southgate's squad for this summer's European Championships. body check tags ::