Anelka, formerly of West Bromwich Albion, was sacked by the Midlands club on Friday, after an ongoing stoush in the aftermath of his controversial goal celebration against West Ham in December.
The Football Association want to ensure the Frenchman still serves his ban, despite his next club potentially being outside England, therefore they have taken their concerns to governing body 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 said.
"We are currently analysing the information and documentation at our disposal."
Anelka fell out with West Brom, after the club demanded he apologise for his gesture - known as 'quenelle' - and also demanded he pay a fine.
The Frenchman did not comply, and told the club he had quit, however the club claimed he did not legally leave and after he posted about the incident on Twitter, the club sacked him on the grounds of 'gross misconduct'.
