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.
West Bromwich Albion have revealed their sponsorship deal with Zoopla was already due to expire in the summer, after the online property firm announced that it would be ending the deal following Nicolas Anelka's controversial goal celebration.
The firm, which are owned by a Jewish businessman, were reportedly unhappy at West Brom's decision to continue to play the French striker despite the controversy over the 'quenelle' gesture which is widely viewed as anti-Semitic.
"West Bromwich Albion has been fully aware since the sponsorship agreement came into force in June 2012 that its partnership with Zoopla could expire this summer and therefore has been planning accordingly," a club statement read.
"Zoopla has today informed the Club in writing that it does not wish to extend its sponsorship deal. The Club will now actively seek a new Official Sponsor for next season."
Anelka is due to play for West Brom in their Premier League game against Everton tonight.
West Brom sponsor Zoopla, who have announced that it will end its shirt deal with the club at the end of the season following Nicolas Anelka's controversial gesture, is co-owned by a Jewish businessman.
The online property firm, which is co-owned by Jewish businessman Alex Chesterman, was reportedly unhappy at West Brom's decision to continue to play Anelka despite the furore over the celebration.
The French striker made the controversial 'quenelle' gesture during Albion's 3-3 draw with West Ham United on December 28.
The gesture, which involves pointing one straightened arm downward whilst touching that arm's shoulder with the opposite hand, has been condemned by Jewish groups as a "Nazi salute in reverse."
Property website Zoopla has decided to end its sponsorship of West Bromwich Albion at the end of the current season after French striker Nicolas Anelka made a controversial gesture against West Ham United.
Zoopla said it had been reviewing its position as the principal sponsor of the Premier League side since the incident during a Premier League game in December.
Anelka sparked controversy when he made a gesture which is widely associated with anti-semitism in France whilst celebrating his goal during the 3-3 draw.
"Through our sponsorship of West Bromwich Albion we are pleased to have supported the local community and charities," Head of Communications for Zoopla, Lawrence Hall said.
"In recent weeks, however, we have decided to re-evaluate this sponsorship and as a result we will focus our attention on other marketing activities from the end of the season.”