Millwall have also reopened an investigation into the incident, saying they are "appalled" by footage shown on Sky Sports News on Monday night.
The film appeared to show the Senegal international alerting the referee, Mark Halsey, and making stewards aware of his allegations but Millwall insisted no complaint of racist abuse was made by the player at the time.
The FA is now investigating the footage - and not just the incident with Diouf. It is understood Leeds have provided the governing body with the Senegal striker's version of what happened.
An FA statement said: "We were concerned by the video footage and we have requested a copy for our full consideration.
"We will work with all the relevant authorities including the police to investigate fully."
The FA also urged anyone "subject to or witness to racial abuse" to report it. Football League chairman Greg Clarke and FA independent board member Heather Rabbatts have both stressed the need for players to be given the support to report incidents of racist abuse.
Clarke admitted something in the game may be "terribly wrong" if black players felt unable to do so.
Clarke, who was at the match in question, told Sky Sports News: "To have our players subjected to such vile and filthy abuse deserves nothing more than the culprits being arrested and facing the full weight of the law.
"There's two issues, one is we have to continue to work with the clubs on our anti-racism programmes which are agreed with the FA.
"Secondly is the reticence of black players to come forward and feel comfortable in supporting it.
"If we've created an environment that doesn't support black players in confronting this issue we've done something terribly wrong.
"We've got to wrap ourselves around our black players and give them our support to report such episodes and then deal with such episodes extremely severely."
Meanwhile, Rabbatts, who coincidentally is a former deputy chief executive of Millwall, said the governing body had to take note of what happened at the Den.
Rabbatts told Press Association Sport: "It's the responsibility of all of us involved in the game that where those incidents take place they are reported so that we can take action.
"It is a real concern that many feel they cannot report such abuse.
"What we saw was shocking and horrible and from the FA's perspective it revealed the challenge that we have still to face in dealing with racism."
However, Reading striker Jason Roberts was dismissive of the FA's recent action plan to deal with racism.
He told Sky Sports News: "We need to do better. We need to have proper zero tolerance to it when these things happen. We need to hit the offending clubs or individuals hard.
"It is also about representation, about having ethnic minorities throughout the game.
"The FA has come up with a 92-point plan but nothing in that plan that makes me think we are going to change this situation.
"When I go out on the football pitch I don't want to be subjected to that kind of abuse. Get CCTV cameras working properly, get the police and stewards doing their jobs properly."
Millwall captain Danny Shittu said he was "deeply saddened" by the Sky Sports News documentary.
He said: "As the current Millwall captain, racism is something I do not stand for or condone. I am currently in talks with the club about any further measures we can take in dealing with and eradicating racism at matches.
"I do not want the events shown yesterday to tarnish the hard work done by the club thus far and their efforts in tackling this issue.
"Every player at all levels has the right to represent their club without being subjected to homophobic or racial taunts. I will do all I can to help eradicate racism at my club and in football."