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 over the singing of a song, which was heard at the World Cup qualifier against San Marino last Friday. The world governing body has 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. And 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."
He added: "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, saying: "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. Always a small minority who ruin it for others. Let's not jump to conclusions + assume though as it might just have been banter. We'll see after the investigation."