Former Arsenal teammate Robin van Persie accused Adebayor of a "mindless and malicious stamp" during the match and he also received a yellow card for deliberately celebrating his goal in front of Arsenal fans.
NEWS: Van Persie accuses Adebayor of stamping
"We'll look at it on Monday and then bring it to the disciplinary process," FA chief Ian Watmore told BBC Radio.
"Our governance team will take a good look at both of the incidents that have been highlighted and will come to the media with the answers early next week.
"The punishments are the decision of the individual commission, if we get that far."
Adebayor, who left Arsenal for City in the last transfer window, was not punished for the alleged stamp but did receive a yellow card for inciting Arsenal fans after running the length of the pitch to celebrate his goal and the home side's third.
"I am sad and disappointed," van Persie said on the Arsenal website. "He (Adebayor) set out to hurt me today. He has shown a real lack of class,"
The Dutch international received treatment for a cut after Adebayor appeared to run his boot down the forward's face.
City manager Mark Hughes defended his new signing after the match.
"We have to cut Emmanuel a bit of slack," Hughes told the club website.
"He is an emotional guy and was caught up in the moment. It was a fantastic goal and great finish. He has already apologised on camera and that is the right thing to do because obviously it can be provocative."
