It has been alleged that the former Chelsea boss clashed with a supporter near the Inter team bus as he left Manchester United's Old Trafford ground on Wednesday night.
Mourinho watched his side suffer a 2-0 defeat at the hands of Sir Alex Ferguson's European champions to crash out of the UEFA Champions League at the last 16 stage.
The police have contacted United to request CCTV footage of the area and have confirmed a complaint has been made.
Investigating"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.
Nemanja Vidic headed the Red Devils into an early lead in Wednesday night's second leg with Cristiano Ronaldo completing the scoring from Wayne Rooney's cross at the start of the second half.
An Inter Milan spokesman later told Sky Sports News that Mourinho had been with club officials constantly from the final whistle until the team landed back in Italy and nothing untoward had been seen.