Television pictures showed Alli's gesture during the 2-1 World Cup qualifying victory at Wembley.
The 21-year-old said it was a "joke with good friend" Kyle Walker.
It is thought the case will not be dealt with until late September at the earliest, BBC reports on Friday.
Tottenham manager Mauricio Pochettino, who also described the gesture as a joke, said Alli was unlucky to be caught on camera and that his general behaviour is fantastic.
Alli and full-back Walker were team-mates at Spurs until the latter joined Manchester City this summer.
The incident occurred in the 77th minute after Alli was body-checked by Fenerbahce defender Martin Skrtel, and referee Clement Turpin waved play on.
It initially appeared that Alli gestured towards Turpin, with whom he also had words when he was substituted in the 93rd minute.