After scoring during the match against West Ham, the Frenchman celebrated by making the gesture - described as anti-Semitic - with one anti-racism campaigner calling for the striker to face a five-match ban.
The FA announced that a decision on whether Anelka will be charged would be made on January 20 at the earliest.
Piara Powar, the executive director of FARE (Football Against Racism in Europe), said recently: "The rules are clear. It is now a minimum five-match ban for any player involved in things related to race or religion.
"We do a lot of monitoring across Europe and we know about the dangers of the Far Right who are very active in football across the continent.
"In Germany it's quite a dangerous term and if we tolerate this then it's just a means of division and going back to almost an era we have seen before and it is dangerous and wrong."
And Powar admits being surprised and disappointed by the lack of an apology from Anelka.
He went on: "Whatever he meant by the gesture, the apology should have been forthcoming immediately.
"The first rule for a player who does something that causes such offence like this is that they should apologise and accept that it might have caused offence. To hide away is just the wrong approach.
"We have also been disappointed to see the delay in the announcement from the FA.
"It feels like it has taken too long really. I don't know why it has taken so long."