Sky sources have confirmed the Portuguese manager clashed with City players after apparently objecting to their post-match celebrations.
Several national newspapers are reporting that Mourinho was covered outside the Old Trafford changing rooms after telling City players to turn down their music.
Police officers and stewards had to separate 20 players and staff, The Guardian reports.
Bottles and punches are said to have been thrown.
City coach Mikel Arteta was reportedly left bleeding from his face from the melee.
The Football Association has asked both clubs for their observations about the incident.
Pep Guardiola’s side moved 11 points clear of second-placed United with the victory.
Mourinho showed no signs of having been soaked when he emerged for his post-match interview with Sky Sports – but it was clear he had not taken the defeat well.
“I think they are a very good team, I think they are lucky, I think (they) have all the decisions in their favour, probably yes,” he said.
The fracas will prompt comparisons with the infamous “Battle of the Buffet” at the same ground when former United boss Sir Alex Ferguson was hit by pizza after his side beat Arsenal 2-0 in 2004.