Bellamy clashed with a fan after the full-time whistle in their 4-3 Premier League defeat on Sunday.
“At the end of the derby between Manchester United and Manchester City at Old Trafford, a member of the public ran on to the pitch, and was detained by police and security staff,” confirmed a police spokesman.
“During this time, there was an altercation between the man and a player from Manchester City FC.
“No formal complaint has been made by either party but police are continuing to make inquiries.”
