Anelka, formerly of West Brom, was sacked by the Midlands club on Friday after an ongoing dispute in the aftermath of his controversial 'Quenelle' goal celebration against West Ham in December.
The FA wants to be certain that the Frenchman still serves his ban, despite his next club potentially being outside England, and has therefore taken its concerns to FIFA.
"We can conﬁrm that the FA have contacted FIFA on the matter and requested the extension of the imposed sanction to have worldwide effect," a FIFA spokesman declared.
"We are currently analyzing the information and documentation at our disposal."
Anelka fell out with West Brom after the club demanded that he apologize for his gesture and also pay a fine.
The Frenchman did not comply and told the club that he had quit - although the Baggies claimed that he did not legally leave and, after he posted about the incident on Twitter, sacked him on the grounds of gross misconduct.