Kolasinac: I have an offer from United
With captain Nemanja Vidic set for Inter, and Rio Ferdinand and Patrice Evra out of contract at season's end, United are in need of defensive reinforcements.
Although United are without a manager following David Moyes' sacking on Tuesday, club officials have identified the 20-year-old Bosnian left back as a transfer target, along with Southampton young gun Luke Shaw.
And Kolasinac, who is the latest Schalke starlet to be linked with a move away from the Bundesliga outfit, said he is considering an offer from the fallen Premier League champions.
"Yes, I have offer from Manchester United," Kolasinac told Bosnian newspaper Dnevni Avaz.
"But, I will not hurry with the decision (over my future). I have to see what Schalke think about it."
The Bosnia-Herzegovina international has made 22 league appearances for third-placed Schalke this season as Jens Keller's men aim to secure automatic qualification for the UEFA Champions League.
Kolasinac has quickly forged a reputation as one of the Bundesliga'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, also made his international debut for Bosnia-Herzegovina in the nation's friendly against Argentina in November last year.