The Football Association fear that England could be ordered to play their next World Cup qualifier behind closed doors as a result of alleged racist abuse aimed at Rio and Anton Ferdinand.
Some fans reportedly sang songs about throwing the brothers on a bonfire, which Football Against Racism in Europe (FARE) believe was racially motivated, during last Friday's 8-0 win over San Marino.
The anti-racism group have made a complaint to FIFA regarding the chants.
Football's governing body have recently banned Hungarian and Bulgarian fans after they were found guilty of racial abuse and the FA fear that they could suffer a similar fate, The Mirror reports.
England face Moldova in their next competitive fixture at Wembley on September 6.