Redknapp was overlooked for the England job earlier in the year, which went to Roy Hodgson, and has since been sacked by Spurs after the failure to deliver Champions League football to the White Hart Lane club.
With Dick Advocaat leaving his position as trainer of the eastern European powerhouses after Euro 2012, the role is up for grabs, with the Russian FA initially keen to hire Roberto Mancini.
However, the Italian has signed a new long-term deal with Manchester City, which could open the door for Redknapp.
“Would Harry have a problem coming to Russia? No. He’s ready to go and live in any country, especially as big as Russia,” his agent Phil Smith told Russian media, translated to English by Sky Sports.
“I think such an offer would definitely interest him if it came, but so far, we haven’t heard anything about it.”
Meanwhile, Fabio Capello is said to be another big-name coach in the running for the role, and his son has confirmed that the ex-England man would be interested in the position also.
“I can say that he would be very interested to become Russia’s coach,” Capello Jnr told Sovietsky Sport.
“My father has always been a great admirer of the Russian team and I know that he would be glad to talk to officials and listen to their proposals.”
By Gareth McKnight