The FA punished Anelka with a five-match ban after the 35-year-oldmade the 'quenelle gesture' in December.
WBA dismissed the player for gross misconduct on Friday, after he claimed to have quit the club on social media.
"The FA has requested the extension of the sanction to have worldwide effect," a Fifa spokesperson told BBC Sport.
"We are currently analysing the information and documentation at our disposal."
The FA's decision to pursue a global ban for Anelka, in an attempt to ensure his suspension will be served should he transfer to a foreign club.
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