Manchester United and Manchester City have been given extra time to provide observations on the alleged fracas following Sunday's derby at Old Trafford.
Runaway Premier League leaders City opened up an 11-point gap over second-placed United with their 2-1 weekend win.
Victory sparked mass celebrations from City, and United are understood to have taken exception to how their visitors conducted themselves in and around the dressing room area.
Milk and water are claimed to have been thrown at United boss Jose Mourinho after a reported confrontation with City goalkeeper Ederson, leading to an alleged altercation involving up to 20 players and staff in a crowded corridor.
The Football Association had been in touch with both clubs, but will now allow until 6pm on December 15 for additional information to be provided.
"Manchester United and Manchester City have both been given extra time to provide their observations following reports of an incident after Sunday's game. They now have until 6pm on Friday 15 December," the FA said in a statement.
United boss Mourinho stood his ground when pressed on the matter at the media conference ahead of Wednesday night's Premier League match against Bournemouth.
The Portuguese coach said Manchester City had showed how different they are to his players.
However, rival boss Pep Guardiola remains convinced his City stars have nothing to say sorry about, having offered an apology which seemed aimed to appease rather than accept any fault.
"The only thing I can say is that for me it was just a question of diversity - diversity in behaviours, diversity in education. Just that and nothing more than that," Mourinho said on Tuesday.
"The diversity of behaviour, of opinion, of education."
He added: "You know, what we did in the Arsenal stadium (after winning 3-1 their earlier this month) it was completely diverse.
"What we did, what happened after that match, the way we behaved as winners... but no problem."
Mourinho wanted to look ahead to Wednesday's match against Bournemouth and was frustrated the derby remained the main talking point.
When asked about possible FA punishment, Mourinho said: "May punish who? Why?"
Mourinho gave short shrift to another reporter bringing up claims that Romelu Lukaku had thrown a bottle in the skirmish, and said: "Show evidence and punish him."
When that was followed up with a question about whether he was confident his players behaved appropriately after the game, Mourinho said: "I know. I am not confident, I know."
City coach Mikel Arteta is understood to have suffered a cut to the face in the skirmish and Guardiola would not confirm any details of the alleged melee.
The Spaniard was adamant his players were well within their rights to try to enjoy their victory in their dressing room, but said he would be prepared to apologise if United considered the celebrations excessive.
"Sometimes Manchester United made a lot, in the past, celebrations over City. It is part of everything," Guardiola said ahead of Wednesday's trip to Swansea.
"But if we were not correct, or something like that, then I apologise to all of Manchester United. Our intentions were not that.
"Our intentions were to celebrate, inside the locker room, our happiness because we were happy. If the people cannot understand that then I'm sorry.
"We were so happy, we won a derby. If in that way we offended United - not just one player, not (just) Jose - then I apologise. We have huge respect for our opponents - not just Manchester United, all the opponents."
Additional reporting by the Press Association.