Arsene Wenger has been asked to explain comments he made about referee Rob Styles by the Football Association.
The Arsenal boss appeared to question the impartiality of the officials in his side's 2-0 defeat by Chelsea.
He said: "We scored a regular goal but the referee made a very bad decision. I associate the referee and linesmen in the same team - the Chelsea team."
An FA spokesman confirmed: "We are writing to Arsene Wenger to ask him for his observations."
The Gunners boss was unhappy after Robin van Persie's goal was ruled out.
He also claimed Styles was not brave enough to send off Chelsea midfielder Michael Essien, who appeared to elbow Arsenal defender Lauren in the mouth in the first half.
"Essien was a straight red in my opinion. It was just in front of the dugout and the referee was not brave enough to make the decision, but it was a straight red," said Wenger.
"He did not play the ball, he played the player. I have played a little football in my life and I tell you that Essien just played the player and not the ball - it should have been a straight red."
Wenger made his remarks after television pictures showed Van Persie had received the ball in an onside position and the goal should have stood, with the score 0-0.
And he was also snubbed by Chelsea counterpart Mourinho, who walked down the tunnel at the final whistle without the traditional handshake.
Reports in Tuesday's newspapers suggested Mourinho was upset that Wenger had not acknowledged an apology which the Portuguese manager wrote in a Christmas card, although neither club has commented on this.
Wenger said: "The first goal is very important and the referee made the wrong decision. For me, our goal was the perfect goal - and it would have changed the game.
"Then they scored and from then on they sat back and hit us on the break, which made it far more difficult for us."
Chelsea boss Mourinho defended Essien by accusing Arsenal of trying to capitalise on his recent disciplinary troubles.
The midfielder was handed a two-game Champions League ban by Uefa last week for his dangerous tackle on Liverpool's Dietmar Hamann in their final Group G clash.
"It was like a strategy to use the image Essien has at the moment," said Mourinho.
"He made his mistake and was punished for that and has a suspension for the Champions league.
"Now I think he deserves to be looked at as a great player and be careful of other teams' reactions in relation to him. That for me is the negative point."
The Portuguese coach then insisted that Arsenal defender Philippe Senderos should have been sent off for fouls on Didier Drogba and Arjen Robben.
Wenger denied Mourinho's claim that he instructed his players to target Essien.
"We didn't even talk about Essien before the game so for a deliberate strategy we hid it very well because I don't know about it," he said.