The striker started for Albion in Monday's 1-1 draw with Everton, just hours after the club's sponsors Zoopla announced they would not be extending their deal due to the striker's actions.
Anelka, who declined to speak to Sky Sports afterwards, has been roundly criticised for making the 'quenelle' gesture - described as anti-Semitic - after scoring against West Ham last month.
If found guilty, the Frenchman will become the first player to be charged by the FA under guidelines introduced to tackle racial discrimination and will face a minimum five-game ban.
Baggies boss Pepe Mel defended his decision to start Anelka against Everton and was happy with the 34-year-old's contribution.
"I spoke with him on Sunday and he said to me that he was ready to play and no more," said Mel. "I have the obligation of thinking in football and what is best for the team."
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."