Rice has long piqued United's interest, with the club identifying him as a top target for their midfield.
They aren't the only team interested in signing the midfielder; Chelsea and Manchester City have also been linked, but have ruled out a move.
Rice has been linked with a move in the last week, with reports claiming the 23-year-old has turned down three contract offers from the Hammers.
His current contract at the London Stadium expires in 2024, with West Ham having the option to extend it for another year.
The Hammers are naturally hesitant to sell their prize asset this summer, with David Moyes previously claiming that selling him would cost more than £100 million before boosting the asking price to £150 million.
Danny Murphy, an ex-Liverpool and Tottenham player, believes the moment is ideal for Rice to make a move. If he were in West Ham's situation, the former midfielder told talkSPORT what he would do.
"Are you going to let another season pass you by without winning the Premier League and the Champions League?" Murphy stated his opinion. "West Ham fans will become irritated if they hear it all the time because I've heard it before." I'm going if I'm him."