Zavarov, who works under head coach Mykhaylo Fomenko, told the channel in a telephone interview that Shevchenko, 39, would bring new ideas into the team's coaching set up.
Shevchenko is Ukraine's record scorer with 48 goals in 111 games and won the Ballon d'Or in 2004 at AC Milan. He retired after Euro 2012 which Ukraine co-hosted with Poland.
Shevchenko was approached by the Football Federation of Ukraine to take over as head coach in November 2012 but declined because he did not have the required coaching qualifications.
That obstacle was removed in March 2015 when Shevchenko, who also played for Dynamo Kiev and Chelsea as well as Milan at club level, completed a two-year programme for a UEFA Pro Licence.
(Editing by Ken Ferris)
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