Griezmann was included on the 30-man shortlist for the coveted individual prize, having finished third for the award in 2016.
The 27-year-old enjoyed another fine campaign with Atletico – scoring 29 goals in 2017-18 as his team won the Europa League – while he netted four times to help France to the World Cup title.
"I wish. He would be a fair winner for me," the Atletico midfielder told RNE on Tuesday.
"Atletico Madrid are growing and are doing so partly thanks to Griezmann. He doesn't have the numbers of Cristiano [Ronaldo] and [Lionel] Messi, but he makes us play and score goals – for his club and national team."
Saul also defended Atletico coach Diego Simeone, who was booed by fans earlier this season.
But the midfielder believes his manager deserves the benefit of the doubt after the amount of success the club have had under his watch.
"With everything he has done and everything he is doing, the doubts are unthinkable," Saul said.