Last month both Paul Pogba and Barcelona’s Ousmane Dembele were subjected to racial abuse from Russian fans during a 3-1 friendly win over their hosts.
It is the third time this season that such a claim has been made following games at Zenit St. Petersburg’s ground, which will play host to one of the semi-finals in July.
The Russian Football Union (RFU) has twice previously faced fines for such charges, brought about by the behaviour of fans at the last two European Championships.
Earlier this week, RFU anti-discrimination inspector Alexei Smertin said the union would do all it can to assist Fifa and that their own investigation was already under way.
“The Russian Football Union is ready to take an active part in it (the FIFA probe) and is already conducting an internal investigation,” Smertin said in a statement carried by Russian news agencies.
“We are looking for the people who were shouting,” he added at a press conference on Monday. “They should not be at soccer stadiums.”
