The West Brom striker made the allegedly anti-semitic action after scoring his side's first goal in a 3-3 Premier League draw with West Ham on December 28.
However, the FA is yet to take any decisive action over the incident, and equality campaign group Kick It Out revealed that, while the delay had left them discontented, they would not be offering their full opinion on the case until it had reached a conclusion.
"Following a gesture made by West Bromwich Albion striker Nicolas Anelka during their game against West Ham United at Upton Park on 28 December, an allegation of anti-semitism was reported by Kick It Out and partner organisations immediately with The Football Association (FA) announcing that it would instigate an investigation," read a statement.
"Since then, in spite of requests from Kick It Out for information about the progress of the investigation, there has been total silence from The FA until Friday 10 January. The FA then stated that an appointed expert was aiding this investigation and there would be no further update until Monday 20 January at the earliest.
"While an investigation is being undertaken, it is protocol for Kick It Out not to comment on matters which might prejudice the outcome and be unfair to any party or individual involved in this process.
"Kick It Out, like others, is very frustrated at the length of time taken to investigate this issue and, as usual, has taken criticism, particularly from community organisations, who feel deeply and rightly aggrieved by the gesture and want to know why the campaign has not made more of a public condemnatory statement of Anelka's actions.
"While Kick It Out can and is prepared to be condemnatory, where it is appropriate, it strives to ensure that it works to counter the prejudices which lead to discrimination and hatred. The campaign will certainly make known its comments on this case at the conclusion of The FA's investigation.
"Kick It Out is totally opposed to all prejudice, discrimination and exclusion in football, and is proud of its commitment to work across all the areas of equality. The campaign is totally opposed to acts of anti-semitism and has no hesitation in condemning such actions. Kick It Out continues to press for an urgent decision."
