The Frenchman has until January 23 to respond to the charge, which the FA alleges relates to an "abusive and/or indecent and/or insulting and/or improper" gesture, which "included a reference to ethnic origin and/or race and/or religion or belief".
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However, Lukaku has defended the West Brom striker and says he does not want to see him banned from playing.
“He was my idol since I was a kid and he still is,” he told the club's official website.
“He shouldn’t have been banned for that. He just likes to support a stand-up comedian in France so we don’t have to make such a big deal about it. He’s an adult.
“For me, I hope he doesn’t get suspended because he’s a player people want to see on the pitch.”
West Brom have announced that Anelka is “considering his options” following news of his FA charge while Albion sponsors Zoopla have revealed they will not renew their sponsorship deal with the club due to the striker's action.