Anelka infuriated members of the Jewish community when he performed the gesture after scoring in the Baggies' 3-3 draw at West Ham on December 28.
The quenelle - which translates literally as "dumpling" in English - is a straight-arm salute with one arm pointing downwards and the other hand across the chest.
It was brought to prominence by the French comedian Dieudonne M'Bala M'Bala, who has been prosecuted for anti-Semitism, and the salute has been described by opponents as an inverted Nazi salute.
The Football Association said last week that a decision on whether to charge Anelka would be made by January 20 at the earliest.
Leading anti-racism campaigner Piara Powar, the executive director of the FARE (Football Against Racism in Europe) network, thinks Anelka can have no defence for his actions and he wants to see the FA implement its new rule of a five-match ban for racism.
"The rules are clear. It is now a minimum five-match ban for any player involved in things related to race or religion," Powar said.
"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."
Anelka has promised not to repeat the gesture again, and he said he views the quenelle as "anti-
system", rather than anything to do with religion. That did not stop a host of critics, including the French sports minister, from attacking the former Chelsea man, though.
Powar has been surprised and disappointed by the lack of an apology from Anelka.
"Whatever he meant by the gesture, the apology should have been forthcoming immediately," Powar said.
"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."
Powar joined fellow anti-discrimination campaigners Kick It Out in condemning the FA for taking so long to decide on whether to charge Anelka.
"We have been disappointed to see the delay in the announcement from the FA," Powar added.
"It feels like it has taken too long really. I don't know why it has taken so long."
The FA has appointed an expert to advise its governance board on the case.
Albion have refused to comment on a report in Friday's Marketing Week which claimed shirt sponsors Zoopla will pull out of its deal if Anelka plays against Everton on Monday.
Zoopla, a property website which is co-owned by a Jewish businessman, also refused to comment.