It was reported in both England and Capello's native Italy over the weekend that Chelsea owner Roman Abramovich was considering replacing Rafa Benitez, who last week criticised both the club's hierarchy and Chelsea fans for not giving him the necessary support.
Capello, who has been repeatedly linked with Chelsea in the Abramovich era, currently manages the Russian national side but it has been suggested he could combine both roles until the end of the season, when interim manager Benitez will leave the club in any case.
Guus Hiddink performed a similar role in 2009 when the Dutchman, also in charge of Russia, arrived as a replacement for Luiz Felipe Scolari and won the FA Cup.
However, Capello says he has not been contacted by Abramovich and is currently happy with the job he has in Russia.
"No offer has arrived from Abramovich, none of it is true," Capello said. "I am thinking about the Russian national team, and I feel very happy in Moscow."
Capello was appointed as Russia manager in July 2012 and his team currently top World Cup qualifying Group F with a record of four wins from four.