The supporter is alleged to have chanted to Mr Mourinho: "You're going home, you're going home".
The Inter manager had just seen his team lose 2-0 to Manchester United to crash out of the Champions League competition.
The supporter later went into Stretford police station, close to Old Trafford, to report the alleged attack.
The fan, who is not from the Greater Manchester area, did not report any injuries to police and did not need treatment.
you don't say!