The 23-year-old is at the top of their wishlist ahead of a return to European football next season.
Rogers has scored 12 goals and provided nine assists across 48 appearances for Aston Villa this season as the club push for a top-four Premier League finish and a Europa League final against Tottenham. Villa value him at a minimum of £86 million, a figure that may stretch United's budget given the scale of their planned summer overhaul.
Aston Villa are prepared to sell if the valuation is met, with a Rogers sale helping the club balance their books under Financial Fair Play regulations. His contract runs until 2031 but he is not expected to agitate for a move.
Chelsea, Arsenal and Paris Saint-Germain are also among the clubs credited with serious interest, meaning United face significant competition. Rogers is a versatile attacker who can operate in central midfield or on the left wing and is comfortable within high-pressing systems — a profile Carrick's United have built their recovery on.
Should a deal for Rogers prove unworkable, the Gazzetta dello Sport reports that United have also held preliminary interest in AC Milan forward Rafael Leão as an alternative option. A FIFA-licensed agent is understood to have made enquiries about the terms of a potential Leão deal, though no formal negotiations have taken place.
United intend to sell up to 13 players this summer, including Marcus Rashford, Jadon Sancho and Joshua Zirkzee, to generate funds for incoming business.