According to the Daily Star, the 23-year-old France international is happy to stay with Real Sociedad despite speculation that continually links him with the Premier League, in particular Liverpool and United.
He's currently with the French national team in Brazil for the World Cup, and in the past has hinted at a move to a big club.
FRIENDSHIP WITH CARLOS VELA
Paris Saint Germain have also been mentioned as potential destination for Griezmann, who bagged 20 goals for Real Sociedad last season alongside former-Arsenal forward Carlos Vela.
Vela was another player linked with a move away from Real Sociedad this summer, but he's signed a new contract after Sociedad after Arsenal worked out a deal on the Gunners' remaining stake in the player.
"He is a top player; this is no better," Griezmann said of Vela. "We have a great relationship on and off the field, because we are good friends," he told ESPN Mexico.
"He is relaxed. He has already signed a new contract and seems happy. I still do not know where my future lies. Hopefully I'll be able to stay, but we have to see what happens."
SCOUTS IN SPAIN
Arsenal, Liverpool and United have all watched the young Frenchman on several occasions, and United even recently came up against him when Sociedad faced United in the Champions League.
His club finished the La Liga season in seventh last term, with Griezmann chipping in with 16 goals and three assists from 35 appearances.
Born in Måcon, France, Griezmann joined Real Sociedad in 2005 as a teenager. He made his first-team debut four years later and is now closing in on 200 league appearances for the Spanish club.
Despite playing through the France youth teams, he only won his first call up for his country's senior squad in February 2014. Four caps and three goals later, and the £25m-rated Griezmann is now an important member of Didier Deschamps' squad.
He started the first game of France's World Cup, a 3-0 win over Honduras, but dropped to the bench for the 5-2 win over Switzerland. Deschamps opted to go with Olivier Giroud and Karim Benzema for the second game.
France face Ecuador in their final group stage game this week.