"Could I play for Real Madrid or Barcelona in the future? Why not," Griezmann was quoted as saying by Marca.
"It is every player's dream to play for a big club like those two or for Bayern Munich.
"But I cannot see myself at Barca or Madrid at this stage, nor at any other club. I am happy where I am now.
"I have no intention of leaving Atletico, not for Paris Saint-Germain, not for China, not for MLS, not for Russia and not for any other destination."
The attacker, who turns 26 on Tuesday, opted to stay at Atleti last year after holding talks with Diego Simeone, but he has made it clear his situation is not necessarily tied to that of the coach.
"My future does not depend on Simeone. He could leave one day or I could leave," Griezmann added.
"I called him ahead of this season to find out what his plans were, he told me he would stay and that felt good, so I also stayed.
"But we are not inseparable."