Manchester United want to sign Griezmann, with some reports suggesting he could cost the Red Devils as much as £100million this summer.
Express Sport understands the France international has been on United manager Jose Mourinho's radar since September, with Chelsea also keen.
Griezmann has already said he is not interested in talking about his future midway through the season.
Paul Pogba and Antoine Griezmann's bromance
Wed, November 9, 2016
Antoine Griezmann has admitted he would like to play alongside Paul Pogba at club level so Express Sport takes a look at their bromance
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Antoine Griezmann has admitted he would like to play alongside Paul Pogba at club level
It seems to have put an end to any suggestion of the 25-year-old leaving Atletico this month.
And Spanish newspaper AS claim the forward has made a point that he is frustrated with being linked with a move away from Spain.
Griezmann scored twice in the 2-2 draw with Athletic Bilbao yesterday.
He ran straight to the nearest camera when celebrating his second goal, shouting “C'est ma maison ici!" (“This is my house here”), which AS claim is in reference to the transfer speculation.
Manchester United want to sign Antoine Griezmann
Griezmann scored twice for Atletico on Sunday
Griezmann is under contract at Atletico until 2021, while his manager Diego Simeone still has 18 months left on his deal.
There had previously been suggestions that both player and manager could move to the Premier League at the end of the campaign.