The London club plans to sign the 18-year-old Ukrainian for 12 million euros. It is known that Ukraine manager Andriy Shevchenko helps make the transfer happen.
Last season, Zabarnyi played 36 matches for Dynamo Kyiv, scoring one goal and making one assist.
Chelsea won the Champions League for the second time after defeating Manchester City 1-0 in an all-English final in Porto on May 29.
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