The Nerazzuri lost 2-0 to, defending champions, United courtesy of goals at the start of each half from Nemanja Vidic and Cristiano Ronaldo.
And it has been alleged that, after the match, the former Chelsea chief punched a supporter near Inter's team coach as they were preparing to leave the stadium.
GMP have contacted Manchester United to request CCTV footage of the area in question, confirming a complaint had been made.
"Shortly before midnight last night a man reported that he had been punched in the face outside Old Trafford," said a police statement.
"We are investigating an allegation of common assault."
Inter have denied the accusation.
"At the end of the game, the Portuguese tactician gave interviews to the European media, signed autographs, watched the penalties of the Roma vs Arsenal game before saluting [Sir Alex] Ferguson in his office," read a statement.
"After giving the last interview to Inter Channel, he entered the team bus that was parked outside the dressing rooms and hence it was a very calm post-game experience."
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