Greater Manchester Police (GMP) confirmed that they are investigating an allegation of common assault.
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The force contacted Manchester United to request CCTV footage of the area and confirmed that a complaint has been made.
A police statement read: "Shortly before midnight last night a man reported that he had been punched in the face outside Old Trafford.
"We are investigating an allegation of common assault."
Manchester United confirmed they were aware of the allegation and were making no further comment.
Mourinho and his team flew back to Italy late on Wednesday night.
They were beaten 2-0 by United, ending their involvement in the competition.
Pre-match hype had heightened tension between Mourinho and his great rival Sir Alex Ferguson, the Manchester United manager.
It is not known if the Inter manager will have to return to the UK to face the allegation.
A spokeswoman for Greater Manchester Police said: At 11.55pm on Wednesday March 11 2009, a man reported he had been punched in the face on Sir Matt Busby Way, outside Old Trafford Football Ground.
"Police are investigating a report of common assault. Inquiries are continuing."
The self-styled "Special One" was approaching the Inter team bus to be ferried to the airport when the alleged incident happened as triumphant United fans milled around outside the ground.
Police have now contacted the club to request CCTV footage of the area.
The fan, who is not from the Greater Manchester area, did not report any injuries to police following the Portuguese manager's alleged punch and did not need treatment.