The latest incident occurred at the end of a damaging defeat for the Reds, during which Suarez was subjected to chants of "cheat" from sections of the home crowd.
Liverpool deserved something - Dalglish
They barracked the player for what they saw as him going down too easily in an attempt to win penalties and free-kicks.
After the match, Reds boss Kenny Dalglish said he had not seen the picture of the hand gesture. "If [it] is true then I've a decision to make," the Scot added.
Dalglish defended the striker over accusations of diving and described the taunts as "scandalous".
He added: "At the end of the day, we will look after Luis the best we can and I think it is about time he got a bit of protection from some people."
The charge against Liverpool concerns the reaction of their players to Spearing's controversial second-half sending-off.
DID YOU KNOW?
Jay Spearing became the third Liverpool player to see red this season in the Premier League - with all having been in London
Five players including Spearing surrounded referee Kevin Friend after he showed the midfielder a straight red for a foul on striker Moussa Dembele with his follow-through after a tackle, having initially won the ball.
The dismissal came after 71 minutes, with the score at 0-0, before Clint Dempsey's late winner sealed victory for Fulham to move them 13th in the league.
Dalglish added: "It is frustrating because nobody tells us what the level of acceptance is. Jay had no other thought on his mind other than to win the ball - and he did win it."
Spearing will miss Liverpool's next three matches after the Reds opted not to appeal against the sending-off.
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