"Comparing 2016 and this year, for me I have to be in the top three," the 27-year-old told French sports daily L & # 39; Equipe.
"In 2016, I lost two finals and was in the top three, this time I won three finals."
When asked if he would not win it would be unfair, Griezmann replied: "It's not unfair, but I wonder what else I can do, I've won three trophies, I've stood out in decisive moments, but it's not me who votes."
Ronaldo and Messi have dominated the Golden Ball in the last decade and the Portuguese superstar will return to compete this year after winning the Champions League with Real Madrid.
But Griezmann, who rejected a move to join Messi at Barcelona next season, admits that ending his dominance over the prize would be special.
"I think about it, especially the closer I get, the Golden Ball is a prestigious prize, and it's the most you can get as a player, there are trophies in your league, in the World Cup, in the Euro, but it's not the same, "he said.
However, there are indications that Griezmann's glorious 2018 in the field may not be enough.
UEFA handed its prize to the best player of last season to Luka Modric, captain of the Croatian team that reached the World Cup final and winner of the Champions League with Real.
And Griezmann was omitted, along with the rest of his teammates from France, from the three final nominees for the FIFA Player of the Year award.
The finalists of that prize are Modric, Ronaldo and Mohamed Salah, the same three who made up the podium for the UEFA award.
When asked about FIFA's rebuff, Griezmann replied: "It's strange, and a shame, it's a trophy presented by FIFA, right?
"And the World Cup is organized by FIFA, right? We won the World Cup, and there is no French player there, that's their choice, but it's surprising that there is not a world champion."
The Ballon d & # 39; Or award was jointly administered by FIFA and France Football magazine until the end of 2016, when the governing body of world football has once again awarded its own prize.
While a panel of supporters, captains of national teams, coaches and journalists vote for the FIFA prize, only journalists vote for the Golden Ball.