However, Real are said to be putting in place a deal to take the 26-year-old to the Bernabeu in the summer of 2018.
Real Madrid are ready to challenge Man United for Antoine Griezmann
Real Madrid want Griezmann to pick up the mantle from Cristiano Ronaldo
The Euro 2016 Golden Boot winner, who will cost around £86m, is seen as the man to pick up the baton from Cristiano Ronaldo.
But Atleti’s move into a new stadium for next season could see him stay at the club for another 12 months.
Griezmann proved his worth to Atletico in today's Madrid derby against Real.
Antoine Griezmann's next club
Wed, April 5, 2017
Which club is favourite to sign Atletico Madrid ace Antoine Griezmann?
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Which clubs are tipped to sign Atletico Madrid ace Antoine Griezmann?
Griezmann scored a late equaliser for Atletico in the Madrid derby
Pepe had given Zinedine Zidane's side the lead shortly after the start of the second half.
But Griezmann popped up with an equaliser five minutes from time to stay third in the table.