The Russian Football Union revealed that 13-man shortlist for the role on Tuesday, with included the Englishman alongside former Barcelona manager Pep Guardiola and ex-England manager Fabio Capello.
Redknapp departed Tottenham last month after failing to secure Champions League football, and spoke immediately of his desire to return to employment at the earliest opportunity in the aftermath.
Speaking to The Sun, Redknapp said: "I haven't been contacted but I'm sure it's a fantastic job for someone."
Dick Advocaat's decision to take the position at PSV Eindhoven came prior to the disappointing Euro 2012 campaign, allowing the RFU to begin their search almost immediately.
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."