The Football Association demanded answers from Manchester United and Manchester City on Monday following reports of ugly scenes that reportedly left City assistant coach Mikel Arteta bloodied after a fracas.
The Guardian newspaper said Arteta was left with blood streaming down his face after a bust-up involving up to 20 players and members of staff from the two clubs after Sunday's Manchester derby, which City won 2-1.
Referee Michael Oliver did not witness the scenes so the FA has not received a report on the matter from him but it has given the clubs until Wednesday to reply to a request for observations following the incident.
United manager Jose Mourinho and City goalkeeper Ederson are reported to have had a confrontation after the game, while it is claimed Mourinho had milk and water thrown at him from the away dressing room.
The home side are understood to have taken exception to City's post-match celebrations.
The Guardian reported that Arteta's eyebrow was split open during the melee in a narrow corridor outside City's dressing room and said there were unconfirmed reports that another member of Guardiola's backroom staff needed medical treatment.
The corridor leading to the dressing rooms apparently became congested as players and staff made their way through it after the game, and tensions spilled over into pushing and shoving, with Arteta understood to have suffered a cut to the head.
Mourinho did not make any reference to what had happened during his post-match media work, according to the report.
Arteta was assessed in the City dressing room after being caught in the crossfire, the report said.
The victory, courtesy of set-piece goals from David Silva and Nicolas Otamendi propelled City 11 points clear of United at the top of the Premier League table, further enhancing their status as red-hot favourites for the title.
Mourinho had accused City's players of diving and committing "tactical fouls" prior to the game and afterwards he made an unconvincing claim his side should have been awarded a late penalty when Ander Herrera was booked for diving.
But City manager Pep Guardiola said: "We won because we were better. In all departments, we were better."
The incident at Old Trafford brought to mind the famous "Battle of the Buffet" that erupted after United beat Arsenal in October 2004, when Arsenal midfielder Cesc Fabregas threw pizza at United manager Alex Ferguson.