Shevchenko gave second and third places to Cristiano Ronaldo (Real/Juventus) and Antoine Griezmann (Atletico Madrid) respectively.
Andriy Pyatov gave second and third places to Cristiano Ronaldo and Mohamed Salah (Liverpool) respectively.
The voting table was published on the FIFA website.
Modric, a 33-year-old Real Madrid midfielder, won the award at the Best FIFA Football Awards ceremony, which took place in London (Britain) late on September 24.
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