The 21-year-old was linked with a number of big-money moves over the summer, but he says that staying with the Txuri-urdin is best for his chances of going to the World Cup with France.
"I want to carry on playing and improving at Real," he told L'Equipe. "It has never been in my thoughts to leave this summer.
"I didn't want to leave and risk not playing at a new club and remaining on the bench.
"My chances of going to the 2014 World Cup would then be slim. Playing at the World Cup is more important to me than moving to a big club."
Griezmann has been capped eight times by Les Bleus at Under-21 level, scoring two goals.