The 25-year-old has an £86million buy-out clause, but that is not set to deter Manchester United in their pursuit.
However, no agreement has yet been reached with Griezmann over his future.
Antoine Griezmann is looking to win trophies with Atletico Madrid
And the striker has outlined he is happy in Spain with Atletico’s projects in his mindset.
The La Liga giants are leaving the Vicente Calderon at the end of the season and will be moving into their new stadium in the summer.
Griezmann hints his future is not a dead certainty, but there are aspects such as winning titles that are keeping him at Atletico.
How Man United could look with Antoine Griezmann
Wed, February 1, 2017
Is this how Manchester United's squad could look with Antoine Griezmann
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Is this how Manchester United could look with Antoine Griezmann
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Atletico Madrid will leave their stadium, the Vicente Calderon, at the end of the season
We’ll just have to see what the future brings
“I feel great at the club and in Madrid,” Griezmann told FIFA.com.
“On a personal level I’m very happy, and in football terms we’re about to move to a new stadium, which is very important.
“We’ll just have to see what the future brings.
Antoine Griezmann is yet to win La Liga, the Champions League or the Copa del Rey at Atletico Madrid
“But for now I’m very happy here and I hope to win trophies with this club.”
But United have made signing the goalscorer their priority for the next transfer window, with a push for Champions League qualification their aim in the meantime to help attract the world’s best.