Pogba played a pivotal role for his nation during this summer's World Cup, as Les Bleus lifted their second trophy with victory over Croatia in the final.
His form at United, however, has been rather more uneven, punctuated by a reported rift with manager Jose Mourinho.
The midfielder nevertheless made the 30-man shortlist for the Ballon d'Or, but believes the prize should go to one of his compatriots.
"Whether it's Grizou (Griezmann), Kylian (Mbappe) or Raph' (Varane), they deserve it much more than me," Pogba told AFP .
"I can not designate one. But I hope with all my heart that this is one of the three.
"One of the four also because there is NG (Kante). That's all I hope for anyway, because there are many who deserve it. I do not put myself in."
France contributed a total of six World Cup winners to the Ballon d'Or shortlist , with Tottenham goalkeeper Hugo Lloris joining Pogba and his outfield companions.
Pogba, meanwhile, is the only representative of Man United to be included amongst the world's top 30.
The award has been won by either Lionel Messi or Cristiano Ronaldo for the last decade , with each star boasting five awards each.
Luka Modric, however, appears a strong bet to break that monopoly after beating Ronaldo to FIFA's The Best award in September in recognition of his efforts with Madrid and Croatia.
The 2018 winner will be announced on December 3 in Paris.