Griezmann enjoyed an excellent 2015-16 campaign, scoring seven goals and 13 games to help Atletico reach the UEFA Champions League final.
The 25-year-old forward also scooped the golden boot as his six goals fired France to the European Championship 2016 final on home soil.
And Griezmann said his stellar efforts in front of goal make him more than worthy of scooping the lucrative individual gong.
"I am proud to be a finalist, that means I am on the right track and have to continue that way," Griezmann was quoted as saying by Croatian newspaper 24sata on Tuesday.
"I don't want to sound arrogant, but I deserve this award because I've had a great season with both club and the national team. It has been an unforgettable season, first in the Champions League with Atletico, then Euros with France," he added.
"Unfortunately, we didn't win a trophy and it was a blow for us, as well as for our fans."
Griezmann faces stiff competition for the award, though, with Ronaldo the current favourite having helped Real Madrid and Portugal claim Champions League and Euro 2016 glory respectively.
Bale also impressed over the course of the last season, playing a key role in Real's Champions League triumph while also inspiring Wales' run to the semi-finals of Euro 2016.