The FA will write to world governing body FIFA on Monday to ask that the five-match ban it imposed for the gesture is served by Anelka at whichever club he may choose to go to next, according to the Press Association.
The FA will also request that the punishment only be considered complete once the player has paid the £80,000 fine issued alongside the ban, and once he has completed an education course.
West Bromwich Albion have said that it "notes Nicolas Anelka is unwilling to agree to the conditions set by it which may have enabled his suspension to be lifted and for him to resume training".
These conditions were, firstly, that the Club required Nicolas Anelka to apologise to it, its supporters, sponsors and the wider community for the impact and consequences of his gesture made on December 28 and secondly, that he accept a substantial fine.
Nicolas Anelka’s purported termination of his Premier League contract this evening via Social Media was invalid as this was not conducted under the correct legal process as required by his contract.
West Bromwich Albion say have not received formal confirmation that Nicolas Anelka has cancelled his contract as they criticised the French striker's claims on Twitter as "highly unprofessional".
Anelka claimed he had left the club to "keep my integrity" on the social network site earlier this evening.
The Midlands club confirmed that it had been in discussions with the 35-year-old as part of its internal enquiry into the 'quenelle' incident and had hoped to conclude its own investigations next week.
"The Club notes Nicolas Anelka’s comments on Twitter this evening (Friday). However, the club has received nothing formally regarding the termination of Nicolas Anelka’s contract from either him or his advisers," the statement said.
"The Club regards the release of such a statement on social media as highly unprofessional and will make a further statement when appropriate."
Nicolas Anelka, who was recently given a five-match ban for using the controversial 'quenelle' gesture, has announced that he has left West Bromwich Albion with immediate effect.
The French striker tweeted his decision, writing in French: "Following discussions between the club and me, proposals have been made to me that I rejoined the group under certain conditions that I can not accept.
"Wishing to keep my integrity, I decided to terminate the contract binding me with West Bromwich Albion until 2014, with immediate effect," the statement concluded.
The Football Association said its Independent Regulatory Commission found Nicolas Anelka guilty of an "aggravated breach" of its rules because the gesture "included a reference to ethnic origin and/or race and/or religion or belief."
But the commission added:
...we did not find that Nicolas Anelka is an anti-Semite or that he intended to express or promote Anti-Semitism by his use of the quenelle.