Rabiot, 27, has emerged as the club's leading candidate following their attempts to sign Barcelona's Frenkie de Jong, per The Athletic.
The France international is into the final 12 months of his contract at Juventus as Erik ten Hag seeks to strengthen his squad ahead of transfer deadline day.
The report claims Man United must decide whether to complete the signing of Rabiot or wait to see how their pursuit of De Jong finishes.
The Dutch midfielder has been the subject of intense transfer speculation, with the player strongly linked with a move to Old Trafford.
Man United would also need to agree personal terms with Rabiot, who is thought to be high on Ten Hag's transfer wish list.
The former Paris Saint-Germain midfielder has been plying his trade for the Italian giants since 2019 and has racked up 129 appearances for the club.
The reports of Rabiot comes after the Red Devils suffered a shock 2-1 home defeat to Brighton on Sunday.
Ten Hag's reign as Man United boss got off to the worst start possible when Brighton went into the break two-nil up.
His team failed to overturn the result in the second-half, with the Dutchman looking at reinforcements before the transfer window slams shut.
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