Football Against Racism in Europe (FARE) have contacted FIFA amid reports visiting supporters directed racist abuse at England defender Rio Ferdinand and his brother Anton.
Last week, football's world governing body forced Bulgaria to play Malta behind closed doors after finding their fans guilty of racist chants during October's World Cup qualifier against Denmark.
And in January, Hungary were fined £27,800 and made to play a World Cup qualifying match against Romania in an empty stadium after FARE lodged a complaint over anti-Semitic chants by their fans during a match with Israel last August.
Three of England's remaining four World Cup qualifiers are at Wembley, with the first on 6 September against Moldova.
FARE's executive director Piara Power said: "We have pulled together evidence sent to us, including media comment, and have passed that on to FIFA.
"It's not really the sort of thing we are generally attuned to looking at - fans abusing players of their own country who may not have been picked.
"We have a duty to report things that are said to us because individuals have reported them as racist or xenophobic. FIFA, in the last couple of incidents, have shown a stronger side. That's quite rare to have a major tournament qualifier behind closed doors.
"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."
It is thought Manchester United defender Ferdinand may have been targeted by some England fans angered by his decision to withdraw from Roy Hodgson's squad for the World Cup double-header against San Marino and Montenegro.
Ferdinand declined the opportunity of a first cap since June 2011 in order to follow a pre-planned fitness routine designed to help him manage his long-standing back problems.
The 34-year-old drew criticism from some fans when he then flew out to Doha to appear as a TV pundit for the San Marino match.