Englishman Redknapp, 65, sacked by Spurs in June, emerged as favourite when Ukrainian Football Federation (FFU) chiefs met on Tuesday, a statement said on the federation's website.
"The praesidium took the decision to begin talks with Redknapp's representatives relating to him working in the post of chief coach of the national Ukraine team," the statement said.
FFU official Mikhail Fomenko, in comments quoted by the website, said Redknapp fitted the bill.
"He has a lot of experience, coaching talent and knows how to motivate footballers," Fomenko said.
"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 England coaches," Fomenko said.
Redknapp enjoyed an eventful four-year spell as Spurs manager, taking them from the bottom of the Premier League to victories over European giants in the Champions League.
He was heavily linked to the England job before the Football Association appointed Roy Hodgson in May.
Ukraine's soccer chiefs first turned to retired striker Shevchenko to fill the post left vacant by Oleg Blokhin who departed to coach top Ukrainian club Dynamo Kiev.
But Shevchenko, 36, who played for AC Milan and Chelsea as well as Dynamo Kiev in a glittering career, turned the job down on Monday saying it was "premature step" for him.
Ukraine sit in fifth place in their 2014 World Cup qualifying group, with two points from three games.
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