Griezmann enjoyed an excellent campaign in 2015-16, scoring 22 LaLiga goals before starring at Euro 2016, winning the Golden Boot with six.
The star 25-year-old forward said his performances were worthy of the prize, despite Ronaldo netting 35 times in the league and leading Portugal to European glory.
“I am proud to be a finalist, that means I am on the right track and have to continue that way,” Griezmann told 24sata.
“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 unforgettable season, first in the Champions League with Atleti, then Euros with France.
“Unfortunately, we didn’t win a trophy and it was a blow for us, as well for our fans.”
Ronaldo also scored 16 goals as Real Madrid won the Champions League, while Bale netted 19 in all competitions while also impressing for Wales at Euro 2016.