With captain Nemanja Vidic set for Inter and Rio Ferdinand and Patrice Evra due to be out of contract at season's end, the Red Devils are in need of defensive reinforcements.
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"Yes, I have offer from Manchester United," the 20-year-old told Bosnian newspaper Dnevni Avaz.
"But I will not hurry with the decision. I have to see what Schalke think about it."
The Bosnia-Herzegovina international has made 22 league appearances for the third-placed Bundesliga team this season as Jens Keller's men aim to secure automatic qualification for the Champions League.
Kolasinac has quickly forged a reputation as one of the German league's most talented youngsters after making his debut for Schalke in a 2-0 win over Greuther Furth in September 2012.
The German-born defender, who can also play in midfield, made his international debut in the a friendly against Argentina in November last year.