"I got a phone call from the RWF (Russian weightlifting federation) and was told to give back my medal," Perepechyonov was quoted as saying by the All-Sport news agency.
Last week, the International Olympic Committee stripped four athletes of their 2004 Olympic medals after retested samples stored for eight years proved positive.
The athletes were men's shot put champion Yuriy Bilonog of Ukraine, women's shot putter Svetlana Krivelyova of Russia and discus thrower Irina Yatchenko of Belarus, who both won bronze, and hammer thrower Ivan Tsikhan of Belarus, who took silver.
The IOC said the fifth case, involving Perepechyonov, was still pending.
The Russian, who won bronze in the 77kg weight class in Athens, has denied any wrongdoing.
"I think they (IOC) are still discussing my case but I have a feeling something is going to happen soon," said the 37-year-old, who retired in 2010.
"I was tested so many times prior to and after the 2004 Games and they found nothing. Now they are telling me they had found some funny substance which is useless for a weightlifter. Where is fair play here?"
RWF chief Sergei Syrtsov said: "We have received a letter from the Russian Olympic Committee, which said that on December 1 the IOC's disciplinary commission discussed the possible breach of anti-doping regulations by Perepechyonov in 2004.
"If he is found guilty, he faces a disqualification from the 2004 Games, and therefore would lose his medal," Syrtsov added.
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