"Today Capello visited the Russian Football Union (RFU) headquarters, conducting negotiations," Russian Sports Minister Vitaly Mutko told local media.
The RFU published a list of 13 high-profile candidates, including the 66-year-old Italian who quit as England boss in February, for the Russia job this week.
"I think during this week or by next Tuesday at the latest, we'll talk with all those coaches on the (RFU) list who would be willing to discuss the offer," former RFU president Mutko said.
Mutko, who is also a member of FIFA's executive board, was not immediately available for comment.
Capello is seen by many as the front-runner for the job, which became vacant after Dutchman Dick Advocaat's departure following Russia's failure to get past the group phase at Euro 2012.
Pierfilippo Capello, Capello's son who also acts as his agent, said his father was interested in coaching Russia.
"I can say that my father would be very interested to become Russia's coach. He has always been a great admirer of the Russian team and I know that he would be glad to talk to (RFU) officials and listen to their proposals," Capello Jr. told the Sovietsky Sport newspaper on Wednesday.
