"It would be better to ask Capello himself if he intends to quit his position as Russia head coach," RFS's general secretary Anatoly Vorobyev said on Friday.
"I think all this information appeared as part of campaign against Nikolay Tolstykh. The psychological attack against him continues. Of course, there is no conflict between Capello and Tolstykh,” he added.
On Thursday, a Russian TV channel quoted a source saying Capello would quit on October 13 if Tolstykh stayed in his role.
The source said that the Italian could resign after the Euro 2016 qualifiers with Sweden and Moldova, which take place on Oct 9 and Oct 12.

It was revealed that Capello and his coaching staff had not been paid for four months, due to the financial position of the RFS.
Vorobyev also complained about the timing of the reports.
"What makes it even worse, perhaps even criminal in regards to football, is that this information appeared on the eve of our qualification games for Euro 2016," he said.
The 68 year-old Capello, who coached England at the 2010 World Cup, took over as Russia coach in July 2012 and took the country to the World Cup finals in Brazil this summer.
However, Russia were knocked out in the group stage, as they managed to pick up just two points from three games.
The Italian has extended his contract with the Russian Football Union until the conclusion of the 2018 World Cup.
According to the Russian press, Capello's new contract means he will earn nine million euros per year.

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