Liverpool captain Jordan Henderson and Arsenal defender Gabriel Magalhaes are facing a FA investigaton.
The incident occurred after the Gunners were awarded a penalty with around 15 minutes remaining.
Reds skipper Henderson and Arsenal defender Gabriel were at the centre of the bust-up, with Granit Xhaka also squaring up to Henderson and grabbing his shirt.
It is believed referee Michael Oliver alerted rivals managers Mikel Arteta and Jurgen Klopp to comments which were made between players in the closing minutes of the game.
The two managers reportedly spoke with the referee after the match too.
Oliver reported the incident to the FA after the game and a review will be launched into the matter, says The Sun.