The France attacker is on-loan with Atleti this season from Barcelona, with the deal carrying a €40m permanent option.
However, Goal says the arrangement includes a second loan season for Griezmann, meaning Atleti can delay shelling out for the striker for another 12 months.
Should Atletico choose to wait, the fee to pay won't change.
For his part, Griezmann has admitted how happy he is to have returned to Madrid this season.
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