Capello was attending Saturday's Russian Premier League match between CSKA Moscow and Rostov after arriving in Moscow on Friday.
"After watching today's match he will go to St Petersburg to see (Russian champions) Zenit in action. Then, he'll return to Italy before coming back to Moscow," Simonyan was quoted as saying by local media. "On Wednesday he will sign a contract and will be presented to the media."
The 66-year-old Italian, who quit as England boss in February, replaces Dutchman Dick Advocaat, whose tenure ended with Russia's group stage exit from Euro 2012.
Capello, who becomes Russia's third successive foreign coach, will be tasked with blooding new players into an ageing team, something his predecessor failed to do in his two years at the helm.
Russian media reported he would earn up to 10 million euros a year after signing a contract through to the 2014 World Cup, with the possibility of extending it for another two years.