Runner Anton Kokorin, who won bronze in Beijing in the men's 4X400m relay team, is the only athlete to have returned his Olympic medal, Yelena Ikonnikova, the anti-doping coordinator of the athletics federation (RusAF), told AFP.
The IOC has ruled that all the athletes who were stripped of their medals over doping violations must give them back.
Ikonnikova confirmed that Russia's athletics federation has received a list of the athletes concerned and passed it on.
"We've distributed the list and the IOC demand for the return of Olympic medals to all the athletes and the regional (athletics) federations concerned," she said.
Ikonnikova added that RusAF has served as a mediator between the Russian Olympic Committee and the international one and the athletes.
Last week Russian Olympic Committee chief Alexander Zhukov said that it "was continuing with its work" to return the medals.
"Although only few athletes have agreed to return medals, we are continuing to work on this. We are contacting them via their sports federations," he told TASS agency.