The salute came to the fore when West Brom forward Nicolas Anelka made the arm gesture when celebrating a goal against West Ham on December 28.
An independent regulatory commission last month handed down a five-match ban to the former France international after finding it "did contain a reference to anti-Semitism" in that it is strongly associated with his friend, the French comedian Dieudonne M'bala M'bala, who has been convicted seven times of anti-Semitic crimes.
West Brom sacked Anelka for "gross misconduct" on March 14 - just hours after he took to Twitter claiming he had decided to terminate his contract - once it was confirmed neither he nor the FA would contest the ban.
The governing body had argued for a more severe sanction and have now confirmed action against four further players after social media posts relating to the quenelle gesture.
A statement released on the www.thefa.com read: "The FA has progressed its investigation into four cases concerning social media postings relating to the quenelle gesture involving Benoit Assou-Ekotto (Tottenham Hotspur on loan at Queens Park Rangers), Yannick Sagbo (Hull City), Samir Nasri (Manchester City) and Mamadou Sakho (Liverpool).
"Having considered the particular facts of each case extremely carefully in consultation with our appointed expert, The FA has today charged Mr Assou-Ekotto and Mr Sagbo with improper conduct contrary to FA Rule E3 in relation to their postings on Twitter.
"It is alleged that in each case the comment was abusive and/or indecent and/or insulting and/or improper, contrary to Rule E3(1). It is further alleged that each players' breach of Rule E3(1) was an "Aggravated Breach" as defined in Rule E3(2), as the comment included a reference to ethnic origin and/or race and/or religion or belief.
"Both players have until April 8 2014 to respond to the charges.
"The FA has issued Mr Nasri with a formal warning. Mr Sakho has been reminded of his responsibilities as a participant.
"As the cases involving Mr Assou-Ekotto and Mr Sagbo are ongoing, The FA will make no further comment on any of these four cases at this time."
Assou-Ekotto, on a season-long loan at QPR from Tottenham, went on Twitter after Anelka's salute to post what translates from French as "I congratulate you on the beautiful quenelle".
Sagbo, who joined Hull from Evian in the summer, also took to the social media network in the aftermath of the incident, posting a picture of Anelka's celebration and a message of support for both the striker and Dieudonne.
The players have until April 8 to respond to charge of improper conduct, which is classed differently to the Anelka case as it was not on the field.
The FA's social media guidelines state: "There are no set sanctions for media comments or social networking comments cases. However, financial penalties are the most usual form of sanction for these kind of cases."
Assou-Ekotto and Sagbo could still face suspension if found guilty but it would unlikely be as severe as the one handed down to Anelka, while Manchester City midfielder Nasri and Liverpool defender Sakho have escaped punishment.
Nasri was pictured performing the gesture and took to Twitter on December 30 to explain his actions.
"The pose in the picture i posted over 2 months ago symbolises being against the system," he said via his account @SamNasri19.
"Its has absolutely nothing to do with being anti semitic or against jewish people. I apologise for causing any hurt to anyone who might have been mislead into thinking this means anything of that nature".
Sakho was also pictured performing the gesture but said in November that he was tricked into performing the gesture.
He wrote on his Twitter account: "This photo was taken six months ago, I did not know the meaning of this gesture, I got trapped!"
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- Nicolas Anelka
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