"As far as we are concerned, nothing happened and there is no truth in it at all," said an Inter spokesman.
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The Italian champions also issued a statement claiming that nothing out of the ordinary had happened after the game: "At the end of the game, [Mourinho] gave interviews to the European media, signed autographs, watched the penalties of the Roma v Arsenal game before meeting [Sir Alex] Ferguson in his office.
"After giving the last interview to the Inter Channel, he entered the team bus that was parked outside the dressing rooms and therefore it was a very calm post-game experience."
Sources said that the United fan, who is from East Anglia, may have been inebriated and it is claimed that he was chanting "Bye bye Mourinho" and "**** off Mourinho" to the tune from the Verdi opera, Rigoletto.
He reported the incident at Stretford police station at midnight, around 40 minutes after Mourinho had left for the airport.
The force contacted United to request CCTV footage of the area and detectives are studying the tapes. Police said the allegation related to a "very minor assault" and the fan was not injured.
A significant number of fans had gathered at the players' exit from Old Trafford after the game. Most of the Inter players had boarded the bus when Mourinho emerged, signed autographs and gave interviews to Italian television stations beside the team bus on Sir Matt Busby Way. The fans are kept at a distance by barriers and a line of security guards.
A spokesman for Manchester United said the club were satisfied it was a police matter and that there was not a breach of security that allowed a fan to get so close to the manager.
Mourinho's Inter were eliminated from the Champions League having lost the game 2-0 – the Portuguese was taunted by United supporters throughout – and he faced some stiff questioning from the Italian media in the post-match press conference. Despite the obvious chill in Mourinho's relations with his inquisitors, he did not lose his temper.
Mourinho had endured a difficult week in the build up to the game.
Having invited the animosity of Juventus manager Claudio Ranieri earlier in the season, he upset many in the Italian game by suggesting Juventus benefit from suspect refereeing decisions and declaring that Roma and AC Milan would finish the season without any trophies.