Reports are gathering pace that the Italian will replace Real Madrid-bound Carlo Ancelotti in the French capital.
“Capello has a contract with the Russian Football Federation,” President Nikolai Tolstykh told R-Sport.
“He has repeatedly talked about how happy he is with the Russian national side and that he intends to continue.”
The 67-year-old, formerly of Milan, Roma, Juventus and Real, is one of numerous tacticians linked with the hotseat at PSG.
Capello has a contract with the Russian national side until the summer of 2014. He was appointed in July 2012.
Fabio Capello’s son was reportedly in Paris on Wednesday for talks.
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