Fabio Capello has said he would be "happy" and "proud" to take the Russia job, Italy's ANSA news agency reported Monday.
The 66-year-old Italian was one of a dozen high-profile candidates for the post, which was vacated by Dick Advocaat after Euro 2012.
A source close to talks told R-Sport earlier this month that Capello would be offered a two-year deal, taking him through the 2014 World Cup qualifying campaign.
"If everything is concluded in the best possible way, as the news from the Russian Federation, I will be happy and proud," Capello was quoted as saying.
"I believe if all goes well as defined by the contract, this will be a wonderful adventure, Russia is a great nation."
Sports minister Vitaly Mutko told R-Sport that Russia would settle on the next coach by Friday.
If confirmed, Capello's first game in charge would be August 15 friendly against the Ivory Coast in Moscow.
He has been unemployed since February, when he resigned from his position as England manager after four years in charge, in protest at interference in team affairs from the country's FA.
Capello has vast experience in the game, winning the Champions League and the Italian and Spanish titles in spells with AC Milan, Juventus, AS Roma and Real Madrid.
Ex-Barcelona coach Pep Guardiola, former Tottenham Hotspur manager Harry Redknapp and ex-Inter Milan and Liverpool boss Rafael Benitez were also named on list of 13 candidates published by the Russian Football Union earlier this month.
