The 26-year-old – who is out of contract at the end of the season – is widely expected to leave the Parc des Princes next month, which has alerted a host of clubs from across Europe.
Chelsea and Tottenham have both been linked with the Frenchman in recent times, but now United have emerged as candidates for his signature.
David Moyes is thought to be desperate to add to his central options in the New Year after watching his side make a below par start to the season.
Despite having spent big to lure Marouane Fellaini to Old Trafford, the Scot’s midfield has looked to be, arguably, the weakest department of his squad.
Matuidi is seen as the sort of player to inject some energy and determination into the Red Devils’ engine room after earning a reputation for his robust and combative style in France.
PSG are likely to accept a reduced fee for their man once the transfer window re-opens, as they set about their own ambitious plans.