Kick It Out chairman Lord Ouseley has called on the Football Association to take a stance on the "vile" and "abusive" chants by England fans aimed at Rio and Anton Ferdinand.
Anti-racism group FARE reported England to FIFA yesterday over the singing of a song, which was heard at the World Cup qualifier against San Marino last Friday.
The world governing body this morning confirmed it was looking at the allegations, which centre on a chant by a section of the England crowd which suggested the Ferdinand brothers should be burned on a bonfire.
It has been suggested the song had racist overtones because Anton Ferdinand was the target of racist abuse from former England captain John Terry.
Ouseley told BBC Radio 5 Live: "Whether it's racist or not, it's certainly unacceptable. It's vile and it shouldn't be part of sport. Something needs to be done about it.
"These are the supporters of the England national team who are travelling abroad and singing songs like that. What messages does it send out about the type of people we are and who we represent?
"The Football Association should be taking a stance on this about the people it wants supporting the England team, the image it wants to send abroad.
"I've already contacted the chairman of the Football Association and said this has to be looked at, investigated and dealt with. Do you want to be having an army of fans who call themselves the England fans travelling abroad, being abusive to their own players like that, or indeed other people?
"FIFA will determine (whether it is racist) but clearly we can take a stance on that. We have policies on anti-racism, homophobia and all other forms of unacceptable behaviour. Why are we so quiet about it?"
FIFA said in a statement to Press Association Sport: "We can confirm that FIFA has been contacted by FARE regarding the FIFA World Cup qualifier match between San Marino and England last Friday.
"FIFA will now analyse the content of the documents and next steps will be determined in due course."
Rio Ferdinand was targeted by fans after withdrawing from the England squad to play in the San Marino game because it did not fit in with his "intricate" and "pre-planned" training programme, although he then travelled to Qatar to commentate on England's 8-0 victory.
The Manchester United defender had been named in the squad for the first time in nearly two years after being left out following the incident between his brother and Terry, although manager Roy Hodgson insisted the decision was made for football reasons.
Rio Ferdinand responded on Twitter this morning:
You expect+accept banter from fans on the terraces as its part of what makes the game great,but racism is not banter,& from ya own fans. WOW
Let's not jump to conclusions + assume though as it might just have been banter. We'll see after the investigation.
Ferdinand's club manager Sir Alex Ferguson feels such extreme reactions are a sign of the times.
He said: "That is the modern society I am afraid. We see a lot of that. Supporters react to many things. I don't think we can change that."
Hodgson has said there needs to be further discussions between the FA and United before Ferdinand could be considered again for his country, but Ferguson is not sure that is necessary.
"I don't think there is any need," he said. "Roy phoned me and I said he would need to speak to Rio for what his reaction is. The matter was put to rest when Rio went to see him."
FARE's executive director Piara Powar conceded it is an unusual case but believes there is enough evidence to conclude the singing was racist.
He told the Press Association yesterday: "Although we did not have observers at the match we have pulled together evidence sent to us including media comment and have passed that on to FIFA.
"I think that it's one of those things that is very subtle. We would say racism and other forms of discrimination is not always banana throwing and monkey chants. It can be very subtle and the people collating the reports believed it is strong enough to send on to FIFA.
"From the reports we have seen I personally think there was an undercurrent of race there, and other people have thought that it has been imbued with racist overtones.
"Whether FIFA think that is strong enough to take action is another question entirely and we accept that it is certainly an unusual report."