The Football Association faced criticism from anti-discrimination group Kick It Out on Wednesday over the time it is taking to deal with Nicolas Anelka's controversial 'quenelle' gesture.
West Brom striker Anelka made the salute after scoring against West Ham on December 28. It is regarded by some in his native France as having anti-Semitic connotations.
The Football Association has appointed an expert to work on the case and has said no statement will be made before January 20.
Kick It Out chairman Lord Ouseley told BBC Radio Five Live the FA should explain why the process is taking so long.
Lord Ouseley said: "They said it would take as long as it needs to take to come to a conclusion. We think that's really bad practice.
"We thought we'd got over that in all our negotiations in the last year. UEFA have demonstrated they can sort a matter out within a week which they did with the CSKA (Moscow) issue that affected Yaya Toure (who was racially abused in the Russian capital).
"The FA itself carried out an investigation within 24 hours when Roy Hodgson was alleged to have made comments regarding monkeys and spaceships and that killed that quite effectively.
"And the Jewish community and the Jewish fans, who believe this has been an anti-Semitic insult and that it should have been resolved, see it as an open-and-shut case, and quite frankly I don't know why the FA's taken so long and is not informing people why it's taking so long.
"An offence was committed in a televised match and there are people who are clearly offended and all the information coming out of France has indicated that the quenelle is anti-Semitic and objected to by Jewish fans.
"We appreciate thoroughness is a necessity but also time, and speed and swiftness, is also important. Because these matters, when they drag on, it leads to all sorts of toxicness that gets into the system and the processes."
Lord Ouseley confirmed Kick It Out is facing criticism itself from those who wonder why the campaigning group has not been "slagging off the FA" and "saying Anelka is guilty".
The 'quenelle' is a straight-arm salute with one arm pointing downwards and the other hand across the chest.
It the was brought to prominence by French comedian Dieudonne M'Bala M'Bala, a friend of Anelka's who has been prosecuted for anti-Semitism, and the salute has been described by opponents as an inverted Nazi salute.
Anelka has agreed not to perform the celebration again after West Brom conceded the gesture had caused offence but the French striker has denied the salute had any anti-Semitic connotations.