The Daily Mail say fines could be imposed after Football Against Racism in Europe (FARE) flagged up to world football's governing body the vile songs which suggested the pair be burned.
The chant in San Marino was: 'Build a bonfire, build a bonfire, put Rio on the top, put Anton in the middle, then burn the f****** lot.'
Football Supporters' Federation chief executive Kevin Miles, who was at the game, said: "Leaping to formal complaint on the basis of second-hand and hearsay information without engaging with supporters' organisations who were present or the FA is not an approach designed to create the best possible outcome.
"The Football Supporters' Federation stand firmly against any manifestations of racism within football. On this occasion, I personally have not heard any of the anti-Rio Ferdinand sentiment being expressed in a way that could be construed as racist.
"Anger about Rio Ferdinand's absence from the squad and presence in Dubai in an Al Jazeera studio was strongly felt and clearly expressed. But I heard no racist content. If there were songs sung with racist undertones, then that is a matter for concern. But even then the response needs to be measured, proportionate and constructive."