The Russia Football Union (RFU) has released an ambitious 13-man shortlist that includes Redknapp, ex-England manager Fabio Capello and former Barcelona boss Pep Guardiola as they seek to replace Dick Advocaat.
Redknapp told The Sun: "I haven't been contacted but I'm sure it's a fantastic job for someone."
Advocaat announced before Russia's disappointing Euro 2012 campaign, when they failed to reach the knockout stage, that he would move to PSV Eindhoven for the new season.
The RFU's list includes high-profile out-of-contract names such as Capello, who has been a free agent since leaving his England post earlier this year, as well as Redknapp, who left Tottenham last month despite steering them to fourth place in the Premier League last term.
Redknapp was favourite to replace Capello as boss of England earlier this year but that job eventually went to Roy Hodgson instead.
Capello has previously also been linked with big-spending Russian side Anzhi Makhachkala, whose former boss Yuri Krasnozhan was included among seven Russian names.
The RFU statement read: "The Russian Football Union has officially informed that the organisation plans to consult, in full compliance with the rules of FIFA and UEFA, the appointment of the head coach of Russian national team, with the following experts: Rafael Benitez, Anatoliy Byshovets, Marcelo Bielsa, Valery Gazzaev, Josep Guardiola, Fabio Capello, Andrei Kobelev, Yuri Krasnozhan, Marcello Lippi, Valery Nepomnyashchy, Nikolai Pisarev, Harry Redknapp, Yuri Semin."
Guardiola's inclusion comes despite the Spaniard having repeatedly stated he would take a year's sabbatical after opting not to renew his Barca deal.
Other major names of the list include former Champions League winner Rafael Benitez, out of work since leaving Inter Milan in December 2010, as well as Italy's World Cup-winning boss Marcello Lippi.