Express Sport understands Griezmann is Manchester United's No1 transfer target for the summer.
Jose Mourinho wants to sign the Atletico star with the futures of Wayne Rooney and Zlatan Ibrahimovic uncertain.
The player has regularly distanced himself from talk over a move to Old Trafford.
How Man United could look with Antoine Griezmann
Tue, February 28, 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
Antoine Griezmann is reportedly considering joining Manchester United
Wayne Rooney and Zlatan Ibrahimovic's Manchester United futures are uncertain
But French newspaper L'Equipe claim the striker is considering joining the Red Devils this summer.
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It is said that United have scouted the player regularly in recent months.
Mourinho believes Paul Pogba, who is close friends with Griezmann, could ensure they land their man.
Antoine Griezmann is currently on international duty with France
United are also mindful of the influence the striker's family could have on any potential deal.
His brother Theo is a supporter of Mourinho's side and could convince his brother to leave Atletico at the end of the season.
Griezmann will now weigh up a move to United and is expected to make a decision over his future in the summer.