"Whether it's Grizou (Griezmann), Kylian (Mbappe) or Raph' (Varane), they deserve it much more than me", Pogba told AFP.
The 27-year-old scored four goals for Didier Deschamps' men in Russian Federation this summer as they stormed to their second world title, beating Croatia 4-2 in the final.
"I cannot designate one".
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Mbappe scored four times in 13 minutes on Sunday but also missed a number of chances, which does not surprise Griezmann.
Real Madrid have two players in the Ballon d'Or nominees - Gareth Bale and Karim Benzema while PSG star Edison Cavani become the final contender. That's all I hope for anyway, because there are many who deserve it.More news: At Ceremonial Swearing-In, Trump Apologizes to Kavanaugh for His ‘Pain and Suffering’
"I wish. He would be a fair victor for me", the Atletico midfielder said.
Despite those strong candidates in the running, Griezmann is adamant that the Ballon d'Or should be given to a French footballer in recognition of the country's achievements over the summer.
"The best team in the world surely possesses the best player, right?"
The Ballon d'Or is run by France Football, after confirmation this year Fifa had broken away from the award.
"In any case, that is how I see it".
Harry Kane and Cristiano Ronaldo have been named on the shortlist for the 2018 Ballon d'Or. Apart from that, it is a question of votes, opinions and different judgements.
The Ballon d'Or, which was first won by Englishman Stanley Matthews in 1956, is decided by a ballot of journalists from around the world.