Traoré is one of the most highly-rated young talents in Serie A and could join in January if talks with Atalanta reach an agreement.
The 18-year-old Ivorian, who has made three senior appearances during his fledgling career, has been closely scouted by United for more than three years.
Traoré recently saw a loan move to Parma fall through, allowing United to pounce and follow up their long-established interest.
United are also attempting to complete a deal for Penarol winger Pellistri.
The 18-year-old Uruguayan is reported to have come by the recommendation of former United striker Diego Forlan, who was Pellistri’s manager before his dismissal from Penarol last month.
Discussions with Penarol over Pellistri are understood to be ongoing, while United are reported to have watched the youngster closely for the best part of a year.