As revealed by The Independent last month, Griezmann has reservations over moving to the Premier League, leaving a switch across the Spanish capital as his only realistic option.
However, the France international believes such a move is unlikely given the historic rivalry between the two clubs.
“I do not rule out anything in the future, but I'm happy at Atletico and hopefully I can stay here,” he said.
“Interest from Madrid? I can't say "yes" or "no". You never know what can happen in football, but moving from Atletico to Real, I don't know if it's achievable.
“Very few players have done so. For this reason, I think it's dead,” he added.
Santiago Solari was the last high-profile player to move from Atletico to Madrid, making the move across the city in 2000.
Several players have turned out as a youth player for one of the Spanish capital’s clubs before switching allegiances, with Raul, the 228-goal Madrid great, being the most famous example.