Rice, 23, has been a standout performer in the Premier League in recent years and has emerged as an England regular under Gareth Southgate.
United are on the lookout for a new central-midfielder to help launch Erik ten Hag’s new tenure at the club and are believed to be keen on signing Rice, whose contract runs out in two years’ time.
However, according to The Mirror, he is set to stay at West Ham for another season, with the midfielder having little desire to move on.
Rice’s decision to remain in east London will be a blow to United who are short in midfield with Paul Pogba and Nemanja Matic set to leave the club on free transfers.
The Red Devils were expected to battle Premier League rivals Chelsea for the West Ham captain’s signature this summer.
However, earlier this year, Hammers boss David Moyes suggested Rice would command a fee of £150 million.
It was thought a deal at £100 million could be agreed for Rice if United were able to stump up the money.
Other central-midfielders on their radar are Barcelona’s Frenkie de Jong and Leeds’ Kalvin Phillips.
But there are reservations about De Jong’s lack of Premier League experience and physicality.
Meanwhile, Phillips is said to be reluctant to join United due to their long-standing rivalry with his hometown club Leeds.
The Manchester giants are also targeting a striker, central-defender and a right-back when the transfer window opens.
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