"It'd be great of a French player won it" the Atletico Madrid star said in an interview with 'Marca' publsihed on Sunday.
"If it's me who wins then even better. But if another Frenchman wins it I will also be proud of them. We had a good World Cup and to win it is very difficult"
Griezmann is one of the 30 nominees for the Ballon D'Or this year, alongside five World champions: Tottenham's Hugo Lloris, Real Madrid's Raphael Varane, Chelsea's N'Golo Kante, Manchester United's Paul Pogba and PSG's Kylian Mbappe.
"We'll see what happens. I can only be happy with the fact that I'm in the running for such an award, but without your team you can't get anywhere, especially when it comes to winning the Ballon D'Or. It would be a dream come true to win it, that's for sure" he continued.
"I'm not the only one who votes, if I was that would make it a lot easier" he joked. "The two previous finals I played in I lost, and on both occasions I blamed myslef for it. I really thought that was the case. But in the last few finals I've been able to make a difference and that's all I wanted to do. You could say that football has been kind to me" he added.
The striker then turned his attentions to his objectives with his club side Atletico Madrid, and in particular the Champions League. The final of the competition will be held at their home stadium, and Griezmann admits they want to be there.
"Reaching the Champions League final is our objective, but it will a difficult task. There are some great team in this year's tournament and we will have to be at our best. That has to be our goal. Maybe this will be our year" the French forward concluded.