Griezmann, who was part of France's World Cup winning squad over the summer in Russia, is currently contracted to Atlético until 2023.
He was heavily linked with a move to both Manchester United and Barcelona over the years but has stayed foot in the red and white side of Madrid.
The forward only turned 27 in March, but has his eye on spending his golden days in the Major League Soccer.
The France international told L'Équipe:
I want to finish my career in the US. I don't know yet if it's going to be in Miami or Los Angeles. Two great cities.
I like the mentality and the show culture of the US.