CSKA general director Roman Babaev has vehemently denied the accusations, claiming that Russian football is the target of a "smear campaign".
However, Jeffrey Webb, who is also the governing body's vice-president, is in London for the Football Association's 150th anniversary and plans on meeting the Ivory Coast international after City's clash with Chelsea to discuss the matter further.
"I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport.
"For me it's about how he felt and I would like to speak to him first to find out what his experience was."
Sunday's encounter at Stamford Bridge is due to kick off at 4pm.