Valentin Balakhnichyov, president of the Russian athletics federation, said Krivelyova was aware of the probe.
"The IOC has notified the Russian Olympic Committee and the ROC then asked us to get in touch with the athlete," Balakhnichyov said.
The IOC is set to discuss potential doping cases from the 2004 Games at its executive board meeting in Lausanne next week, an Olympic movement source said on Monday.
Krivelyova was awarded the bronze medal in the women's shot put in Athens after her Russian team mate Irina Korzhanenko was stripped of her gold after failing a drugs test for the anabolic steroid stanozolol.
"I'll just tell them to go to hell If they come and ask for my medal," Krivelyova, 43 and who has long retired from the sport, was quoted as saying by Russia's All-Sport last week.
"I've been in the sport for 20 years and I've never done anything against the rules. Usually, it was quite the opposite - I was often awarded somebody else medals after they had committed doping violations."
Krivelyova, who won gold at the 1992 Barcelona Olympics and the 2003 world championships in Paris, also claimed the 1999 world indoor title after initially finishing third.
She was promoted to the gold-medal position when the first two athletes, Ukraine's Vita Pavlysh and Korzhanenko, were disqualified after testing positive for stanozolol.
Krivelyova also benefited when Pavlysh was stripped of her 2004 world indoor title after testing positive for stanozolol for the second time. The Ukrainian was then banned for life.
Five suspect doping samples from the 2004 Games were discovered by the IOC in July during more sophisticated re-testing of samples for already-known substances.
The IOC has not named the athletes involved.
The re-testing of samples was introduced after the 2008 Beijing Olympics.
The IOC has an eight-year statute of limitation for taking away medals and amending competition results in case of positive tests or evidence of doping during Olympics.
Krivelyova has denied any wrongdoing.
"Why they're trying to prove me guilty after all these years. Why not wait another eight years - maybe by then they could discover something else?" she said.
"I'm not going to give my medal back. You can count on it. Why should I give it to someone who initially finished fifth (in Athens) and, unlike myself, was never tested," she added.
"This whole thing is a complete and utter nonsense."
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