The Italian was unable to guide the nation out of the group stage of the World Cup this summer but will see out his contract.
The Italian led the Eastern Europeans to the tournament in Brazil this summer but could not get out of a group containing Belgium, South Korea and Algeria.
But Capello will remain in charge until 2018, when Russia hosts the competition, and Vitaly Mutko says he has the chance to win the hearts of the Russian people.
"If the tournament is a success in 2018, we'll bury him next to Dostoyevsky," he told reporters.
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Capello, meanwhile, is already looking ahead to the 2016 European Championship, but acknowledged his priority is the next World Cup.
"The main goal is the World Cup, but first we have to qualify for Euro 2016 in France," he said. "I will remain coach until 2018. I never said that the goal was to reach the quarterfinals in Brazil. We prepared well but I always considered us one of the outsiders."
Capello also took time to dismiss reports that he fell out with certain members of the squad during the campaign this summer.
"I have read about what I was alleged to have told the players, but never in my life and career have I spoken like that to my player. I'd be a fool if I did that."