Reports in Spain suggest the France international could quit the La Liga side with Manchester United and Bayern Munich circling.
Barcelona were interested in signing Griezmann last summer but he decided to renew terms with Atletico.
The winger even made his own documentary highlighting how he had come to his decision.
But Spanish outlet Sport now claim Griezmann is ready to quit the club after a disappointing season both in La Liga and the Champions League.
The reports claim 27-year-old was promised a competitive team by Diego Simeone.
Thomas Lemar joined the club with Lucas Hernandez signing a new deal but Atletico are 10 points behind Barcelona in La Liga.
Lucas and Diego Godin are both thinking about leaving the Spanish outfit – another factor in Griezmann considering his future once again.
Manchester United are the frontrunners for his signature.
Griezmann has never hidden his ambition to play for the Red Devils and with international team-mates Paul Pogba and Anthony Martial at Old Trafford a move could be on the cards.
Paris Saint-Germain would also have the resources to sign the forward.
Griezmann has been in good form again this season, netting 18 goals and providing eight assists to his team-mates in all competitions.
But with Atletico being dumped out of the Champions League by Juventus, the Frenchman is reportedly looking for a move.
United will look to strengthen their side this summer after a disappointing campaign.
Ole Gunnar Solskjaer is in charge until the end of the season after he replaced Jose Mourinho.
And such has been the form of United since the Norwegian has taken over, he could be handed the job on a permanent basis.
Tottenham manager Mauricio Pochettino is also in the running.
No decision on Griezmann would likely be made until a permanent boss is appointed by United.