International gay rights group AllOut said Russian campaigners asked Bach in Paris on Saturday "to launch an independent investigation on the legal implications of the anti-gay laws in effect in Russia during the Olympic Games."
"A list of precise questions about the implication of the anti-gay laws, to help frame the investigation, were submitted and received by the IOC president," AllOut said in a statement. "The IOC will announce later whether or not the investigation will be done."
The International Olympic Committee and its sponsors have been pressed to take a stronger position against Russia after President Vladimir Putin signed a law in June banning promotion of "nontraditional sexual relations" to minors.
"The IOC must call for an end to the discriminatory laws and ensure that the Olympics never again take place in a city where athletes are silenced because of who they are or who they love," AllOut executive director Andre Banks said.
The IOC has previously said Moscow assured that athletes and spectators will not face discrimination at the Feb. 7-23 Winter Games.
Bach, an Olympic gold medallist in fencing, was in Paris to attend a centenary party for the sport's governing body.
The IOC issued a statement Saturday noting Bach's meeting with France President Francois Hollande at the Elysee Palace, though it did not refer directly to the issue of gay rights.