The governing body of football in England had been looking into allegations that racially-motivated chants had been sung by England supporters about the pair during their World Cup qualifying win in San Marino.
"We've been asked to supply our submission to FIFA by Tuesday, which we will do," said Adrian Bevington, the FA managing director of Club England .
"We have gone through all of the video evidence that our security team recorded on the evening of the game.
"I do want to make clear that while the journalists who have reported this have done so in good faith, they clearly have heard some chanting of a particular nature, and we're not disputing that, but we haven't been able to identify any of that from the recorded evidence that we've gone through."
Rio Ferdinand had come under fire for withdrawing from the England squad citing a fitness programme, only to then appear on television in Qatar as a pundit for the match.
Football Against Racism in Europe had brought the offensive chants to FIFA's attention in the aftermath of the match.
FIFA will take the FA's letter into consideration when they come to review the case, but can decide to bring forward a charge, which if upheld could lead to a fine or even a home qualifier played behind closed doors.
"It's not for me to predict what FIFA will or won't do," Bevington added.
"We are dealing with a very small number in an isolated incident here. And it's not something, thankfully, that we have experienced problems with for a long period of time now.
"I certainly wouldn't shy away from addressing anything that is a problem. But, likewise, it's also equally as important that we do praise the vast majority of our fans who sometimes can be tarnished by the behaviour of a very, very small number of people."