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The Frenchman arrived at the Camp Nou from Atletico Madrid in 2019 and he hasn't managed to fully settle yet.
He still has three years remaining on his deal and now 30-years-old, Griezmann is keen to fulfil a lifelong dream.
Griezmann told Le Figaro per Goal: "I still have three years to go. I have to pay attention to my body, because at any time it can change.
"My contract with Barcelona runs until June 2024 and after that I think it will be the right time to go to the United States.
"I love this country, the culture, the NBA and the desire for adventure attracts me, but I also have a family that I would have to move out there.
"I would like to end my career there but still be good enough on the pitch and win MLS, instead of coming in with nothing to give and looking like nothing on the pitch. That wouldn't make sense."
Despite it being a poor season for Barcelona domestically, Griezmann managed to finish as their second top scorer behind Lionel Messi.
Griezmann is currently away with France at Euro 2020 and they're big favourites to win the tournament.
Didier Deschamps guided 'Les Bleus' to World Cup glory in 2018 and Griezmann played a key role in that tournament.
He came third in the 2018 Ballon d'Or rankings thanks to his performances and Deschamps is a big fan of the player.
In fact, he's gone as far as calling the former Real Sociedad man one of the greatest ever.
According to Football 365 he said: "Above and beyond the fact that he's playing in consecutive games, and wonderfully so for him, for all his game-volume, he may not be 20 years old anymore, but he takes very good care of himself.
"He's a professional and he's managed to avoid the different injuries that he could have had. The statistics speak for themselves.
"You can see the influence that he has for the French national team, through the goals that he scores, through his assists.
"If we then add to that the capacity that he has to change the game, to get stuck in when we need to defend when we don't have the ball, he's one of the greatest players of all time, both in Europe and worldwide."
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