Anelka will remain available for selection while he considers his options after being charged by the Football Association over his controversial 'quenelle' goal celebration.
Under new FA rules, such aggravated offences carry a minimum five-match ban and possibly a longer suspension.
In a statement West Brom said there would be no action from them until the FA had concluded their disciplinary process.
"Anelka has received a 34-page document explaining the allegations against him and informing him that he has until 6pm on Thursday to respond. The player is now considering his options.
"Under FA rules, Anelka remains available for first-team selection until The FA's disciplinary process has reached its conclusion. Following this, the club will conclude its own internal enquiry."
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