The ex-Barcelona boss and former England manager are on a 13-man shortlist to fill the vacancy left by the Dutchman following the team's disappointing Euro 2012 campaign
Guardiola stepped down from his post at the Catalan club following the conclusion of the 2011-12 season, citing exhaustion as a major factor in his decision.
The former Spain international will take a one-year sabbatical from football but that has not stopped the Russian FA from making him a candidate for the job.
Other names on the shortlist include ex-Tottenham boss Harry Redknapp and Zenit St Petersburg coach Luciano Spalletti, who recently revealed he would be honoured to take the job.
Russia failed to reach the knockout stages of Euro 2012, finishing third in Group A behind Czech Republic and Greece.