The rumours come in the wake of Benitez's outburst against his 'interim' title and the fans who have been hostile towards him since his appointment following the sacking of Roberto Di Matteo.
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"I have not received an offer," he told Radio Anch'io Sport.
"I'm thinking about the Russian national team, and I feel very happy in Moscow."
The reports from Italy echo the Guus Hiddink situation back in February 2009 when, then the coach of Russia also, the Dutchman took over at Chelsea on a short-term contract following the sacking of Luiz Felipe Scolari.
Hiddink went on to be a popular figure at the club, winning the FA Cup with a 2-1 victory over Everton.
Capello, who has managed several of the top sides in Europe, including Real Madrid, Roma, Juventus and AC Milan, accepted the Russia job following Euro 2012 and has led his new team to four wins out of four games in qualification for the 2014 World Cup in Brazil.