Griezmann, speaking with L'Equipe, believes last season was the best of his career.
"It's the most successful. I've scored more goals but in terms of trophies, it's the best," he said.
"It's strange and a bit of a shame. This is a FIFA trophy, right? FIFA organises the World Cup. We won it and there is not one France player on the final list.
"Yeah, I think I'm getting closer all the time. The Ballon d'Or is a prestigious award and is the peak for any player. There's nothing higher.
Asked if he'll never win it, Griezmann added: "It won't be unfair, but I'll wonder what else I have to do. I've won trophies and was decisive at key moments. But then I don't vote."