The former Tottenham boss has confirmed his interest in the vacant position and his agent, Paul Stretford, is currently holding discussions with the Ukrainian FA
The 65-year-old was widely acknowledged as the favourite for the England manager's job following Fabio Capello's sacking in February, but was overlooked as Roy Hodgson was appointed.
After Tottenham then missed out on Champions League qualification by virtue of Chelsea's victory in the competition, the Englishman was relieved of his duties at the north London club.
But, having been out of work for a matter of months, Redknapp is keen to take on another challenge, and would come up against the Three Lions in World Cup qualifying should he be handed the role.
He told the Daily Mail: "It's a fantastic job. I found out about it a couple of weeks ago when they got in touch with my advisors. I am serious about it.
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"I will talk to them and see if we can sort something out. I'm definitely interested, without a doubt."
Redknapp's agent, Paul Stretford, was in Ukraine on Wednesday to hold discussions with the the Ukrainian football federation about his client's availability.
Mikhail Fomenko, of the UFF, said: "He has a lot of experience, coaching talent and knows how to motivate footballers. In whatever team he led Redknapp very quickly improved the quality of the play and achieved significant progress.
"Today he is an expert in the game and one of the best English coaches."
Ukraine have been without a manager since Oleg Blokhin quit to take the reins at Dynamo Kiev.