It has been alleged Mourinho punched a supporter close to the Inter team bus as he left the stadium following his side's 2-0 defeat.
GMP have contacted United to request CCTV footage of the area and have confirmed a complaint has been made.
"Shortly before midnight last night a man reported that he had been punched in the face outside Old Trafford," a police statement read.
"We are investigating an allegation of common assault."
United would only confirm they are aware of the allegation and are making no further comment.