Kolasinac has impressed at Schalke this season and United are thought to have identified the full-back as a possible replacement for Patrice Evra.
The Bosnia-Herzegovina international claims he has an offer on the table from United, but that he is in no rush to make a decision on his future.
"It is true me and my club both got an official offer from Manchester United," Kolasinac told Bosnian newspaper Dnevni Avaz. "But at this moment I wouldn't like to talk much about this.
"My manager knows all about this offer from England and together we will think and then make a decision.
"I will take my time, I will not hurry.
"I have to think seriously about an offer like that and of course the Schalke board have to think about it."