The FA will decide whether to investigate the incidents which occurred in the tunnel at Old Trafford on Saturday after they receive referee Phil Dowd's match report, according to The Express.
The police were called and they, along with stewards, had to keep Manchester United and Liverpool players apart following the game, which United won 2-1.
"There was a bit of commotion in the tunnel but the referee came in and told us to keep our heads," said United defender Jonny Evans.
The fracas occurred minutes after Patrice Evra celebrated the win with United fans, directly in front of Luis Suarez.
In 2006, the FA fined Gary Neville £5,000 for provocatively celebrating in front of Liverpool supporters.
