Suarez charged over finger gesture at Fulham
Liverpool lost the game to a late strike by Fulham's Clint Dempsey and Suarez was filmed pointing his middle finger towards the Fulham fans as he walked off the pitch.
During the match the home crowd were often heard shouting "cheat" at the Uruguayan forward.
Suarez was already in hot water with the authorities after he was charged by the FA with racially abusing Manchester United left-back Patrice Evra during a 1-1 draw at Anfield in October.
The FA also charged Liverpool with "failing to ensure its players conducted themselves in an orderly fashion" following the sending-off of midfielder Jay Spearing during the Fulham game.
Suarez and Liverpool have until December 12 to respond to the charges.