Anelka was recently given a five-match suspension by the Football Association for his controversial 'quenelle' gesture and dramatically announced on Friday that he would not play for Albion again.
Via his Twitter account, he announced he had quit the club following talks.
West Brom have now moved to insist that they have not terminated his contract, and that they regard Anelka's announcement as 'unprofessional'.
The Baggies statement read: "The Club confirms it has been continuing discussions with Nicolas Anelka and his advisers as part of its own internal enquiry into the gesture he made after scoring against West Ham United on December 28.
"Following the conclusion of the FA's enquiry into the same incident, the Club 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 Club regards the release of such a statement on Social Media as highly unprofessional and will make a further statement when appropriate."
Anelka was charged by the FA with misconduct and found guilty after a two-day hearing at the end of February following the 'quenelle' incident.
An independent regulatory commission however accepted there was no intent by Anelka to be anti-Semitic. West Brom also fined him £80,000 and he was ordered to complete a compulsory education course.