Reports have suggested that Three Lions fans were chanting about the Manchester United midfielder and his brother Anton during the national side's game in San Marino last week
It has been alleged that sections of the travelling support were chanting in a racist manner about the Manchester United defender and his brother Anton, and the FA confirmed that it will continue to search for evidence and punish anyone found responsible.
In a statement, Club England MD Adrian Bevington explained: "In San Marino, we had FA security officers monitoring the English supporters in the stadium. This includes recorded video footage.
"While we have no reason to dispute the media reports which are without doubt made for the right reasons of fighting racism, at this time we have not found any recorded evidence of the specific discriminatory chanting referring to Rio and Anton Ferdinand and the vile 'bonfire' song.
"We will of course continue to review all of our recorded footage. We recognise the importance of Football Against Racism in Europe's responsibility to report any incidents to Fifa.
"We will liaise with Fifa and work with them to assist any investigation. Should evidence of any racial chanting be found, we would expect action to be taken against any individuals.
"The FA would terminate England fans' membership of any guilty members, while we would expect banning orders to be issued by the courts as a minimum penalty.
"We do not want supporters who chant vile or racist abuse following the England team.
"The FA will continue to work closely with Kick it Out and Fare to ensure we do all we can to eradicate racism from football. We fully recognise that we must continue to address any issues that arise involving our own supporters in the same manner we expect other nations to do so.
"However, we will not accept any racist chanting and we also call on those attending England matches at home and abroad to stop the 'No Surrender' chanting during the singing of the national anthem, both before and during games.
"We have made significant progress following the hooliganism that blighted the national team in 1998 and 2000. We must continue to maintain this hard work."