The FA have launched an investigation into the tunnel scrap that left Mikel Arteta with a cut to the head after Sunday's Manchester derby, the Telegraph have reported.
A melee broke out after United players and staff reacted angrily to what they perceived to be excessive celebrations from the victorious City players.
Milk and water was thrown in the direction of Jose Mourinho, while punches were reportedly thrown.
“The FA have sought observations from both clubs in relation to an incident which occurred following yesterday’s game,” the FA said.
Both clubs have been given until 6pm on Wednesday to respond to the FA, before the governing body looks into potential sanctions and further investigation.
Referee Michael Oliver is understood not to have witnessed the incident and did not mention it in his match report.
It is not being investigated by Greater Manchester Police, although an officer was required to break up the skirmish.
United's players and staff were reportedly furious at the "raucous" celebrations of City's players after the 2-1 win, with Jose Mourinho accusing goalkeeper Ederson of lacking "respect".
Tensions boiled over when Mourinho reportedly confronted Ederson, and said: “You f***ing show respect. Who are you?”
City's players roared back in support of the goalkeeper, as Mourinho shouted: “Show some respect! Show some respect!”
The incident reportedly lasted around two minutes, before Mourinho escaped to the referee's room and attended his post-match press conference, in which he made no mention of the fracas.
The Portuguese coach was furious at the decision not to award his side a penalty when Ander Herrera went down in the box.
"My first reaction is I feel sorry for Michael Oliver because he had a very good match but unfortunately he made an important mistake," Mourinho told BBC Sport.
"The result was made with a big penalty not given. That would have been 2-2. Michael was unlucky because it was a clear penalty.
"Manchester City are a very good team and they are protected by the luck, and the gods of football are behind them."