Metro is reporting that the Red Devils are interested in signing the 19-year-old defender as the January transfer window draws nearer.
According go the same story, Manchester United sent scouts to watch the young defender in action for the Hammers during their 4-0 loss to the defending champions.
The same article claims that Chelsea FC are also keen admirers of Rice, whose current contract at West Ham is set to expire in the summer of 2020.
It goes on to say that Manchester United have been impressed by what they have seen of Rice and that they have been monitoring his progress closely this season.
Rice has made 10 Premier League starts for West Ham United so far this season under Manuel Pellegrini.
Manchester United, who will take on Young Boys in the Champions League on Tuesday night, are likely to be linked with a host of players in the lead-up to the January transfer window.
The Red Devils are currently in seventh place in the Premier League table and 14 points behind leaders Manchester City after 13 games of the new campaign.
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