The Frenchman has been linked with a move away from Atleti for some time, with some of the top European clubs reportedly interested in his services.
"Could I play for Real Madrid or Barcelona in the future? Why not," Griezmann said in a Q&A with L'Equipe. "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."