The former Spurs boss is on a 13-man shortlist to fill the vacancy as Russia looks to improve following a disappointing Euro 2012.
Redknapp took over at White Hart Lane in 2008 with the club bottom of the league and enjoyed a successful spell helping to guide the team to fourth spot in the Premier League in his final season in charge.
Shortly after his axing on June 13, the 65-year-old confirmed his ambition to return to a managers role soon and has been named on a 13-man shortlist by the Russian FA.
Russia failed to reach the knockout stages of Euro 2012, finishing third in Group A behind Czech Republic and Greece.
Others names on the shortlist include former England boss Fabio Capello and former Barcelona coach Pep Guardiola.
A number of others names have been linked to the role including former Roma boss Luciano Spalletti who revealed he would be honored to take over.
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