Kick It Out (KIO) has asked Fifa if it has taken any action over a video posted on social media by Chelsea's Enzo Fernandez last year featuring an alleged "racist and transphobic" chant.
The anti-discrimination group says if no investigation has taken place by world football's governing body "it points to a deeply concerning lack of transparency and accountability".
The footage showed the midfielder and some other members of the Argentina squad singing a derogatory song about France's black players after winning the Copa America in July.
In a letter sent to Fifa president Gianni Infantino - and seen by the BBC - KIO's chief executive Samuel Okafor wrote: "Despite making inquiries to the FA and Fifa, we and many others have not been told if there has been any investigation or outcome into his or any other players' conduct.