Manchester United midfielder Paul Pogba and Barcelona winger Ousmane Dembele were allegedly targeted by racist chanting during the match in Saint Petersburg last month.
"We have no further comment at this stage," the FIFA spokesman told AFP.
The Russian Football Union (RFU) said it was ready to cooperate with FIFA's probe.
"We launched our own internal investigation the day after the match," RFU anti-discrimination officer Alexander Baranov said.
"All international matches are played under the jurisdiction of FIFA. We opened it to understand what happened for ourselves. We have sent inquiries to the interior department."
Baranov added that the RFU was "in dialogue with FIFA. We are ready to send them our findings -- there is no problem there".
Russian football chiefs are under pressure with just two months to go before the start of the World Cup on June 14 as the domestic game has been once again tarnished by incidents of racism and hooliganism.
"These people should not be allowed into stadiums. They should not be giving the world reason to think there is racism in our country," added Alexei Smertin, head of the RFU's anti-discrimination department.