The Football Federation of Ukraine revealed in a statement on Tuesday afternoon that they would seek to begin talks with Redknapp to succeed Oleg Blokhin.
The 65-year-old has been out of work since leaving Tottenham in the summer. He has since turned down an approach from Russia, who subsequently appointed former England boss Fabio Capello.
According to the FFU statement Redknapp's name was agreed as its first choice - after Andriy Shevchenko turned down the role on Monday - following a recommendation from former Arsenal defender Oleg Luzhny, who manages in the country's Premier League.
Redknapp, 65, told the BBC: "It is interesting. It is an exciting country with some good young players and some great teams and I am serious about it."
The Sun reported on Wednesday that a deal for Redknapp would see him paid up to £6 million, plus bonuses.
However he has also been linked with the manager's job as the Premier League's bottom club Queens Park Rangers, where Mark Hughes seems to be on borrowed time - and there are suggestions that Redknapp and his advisors could use Ukraine's interest to prompt the Rs into action.
The FFU stated: "On Tuesday, during a meeting of the Football Federation of Ukraine, the chairman of national teams' committee and coaches' council Mikhail Fomenko reported on the situation surrounding the selection of candidates for the position of a head coach.
"During discussions some specialist managers were suggested to be invited from England - Oleg Luzhny and Yury Vernidub mentioned Redknapp's surname.
"The majority of members of the committee supported this suggestion.
"The presidium made the decision to start negotiations with Redknapp's representatives concerning his work on the position of the head coach of a national team of Ukraine."
Ukraine, who are in the same World Cup qualification group as England, have been looking for a new manager after Blokhin resigned to take over at Dynamo Kiev earlier this season.
Shevchenko, 36, turned down the chance to coach his country after claiming any such move would be a "premature step".
Redknapp would bring inside knowledge of the England team. He was tipped by many to take over following the departure of Fabio Capello - with even players tweeting their support for his appointment - before the FA opted for Roy Hodgson and he later left Spurs.