Figures from United apparently took exception to the raucous manner in which City were celebrating their 2-1 success, which included playing loud music in their dressing room.
The corridor leading to the dressing rooms apparently became very congested as players and staff made their way through it after the game, and tensions spilled over into pushing and shoving.
City coach Mikel Arteta is understood to have suffered a cut to the head in the fracas, while Mourinho apparently shouted into the City dressing room.
There have also been reports milk and water were thrown at Mourinho.
Neither club commented when contacted by Press Association Sport on Sunday evening.
The incidents occurred after a fiery end to the match. There were arguments among players after United had a penalty appeal rejected in the latter stages.
City won with goals from David Silva and Nicolas Otamendi, with Marcus Rashford replying for United. The victory was City's 14th in succession in the Premier League and extended their lead at the top of the table to 11 points.
Mourinho conceded afterwards that City's advantage in the title race was now at a "significant distance".
Asked if it could be clawed back, he said: "I don't know. We are going to work and fight for it. That is the only thing I say."
Mourinho complained about the late penalty decision, which saw United's Ander Herrera booked for diving after a challenge by Otamendi.
"It is a huge penalty in a crucial moment of the game," said Mourinho, who also bemoaned his side's luck.
City boss Pep Guardiola had no time for Mourinho's complaints.
"We won because we were better, in all departments," Guardiola said.