The France star will be one of the most wanted players in the transfer window this summer with the likes of Manchester United interested in the 26-year-old.
But the eve of the Madrid derby later today, reports in France suggest a sensational deal could be on the cards.
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?
Respected newspaper L'Equipe claim Real intend on trying to sign Griezmann in 2018.
It's said Griezmann will wanted as the long term replacement for Cristiano Ronaldo.
However Griezmann adviser Eric Olhats said earlier in the week that a move to arch-rivals Real was "impossible".
Atletico Madrid star Antoine Griezmann
He said: "It's impossible, there's a non-aggression pact, there's a deal between the two clubs that does not touch each other.
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“It's not on the agenda. Between the two clubs, there's something that's been around for a long time."
While Griezmann has spoken out over his frustrations with the transfer speculation.
The front page of L'Equipe
He said: “It's always the same question and I now don't know what to say.
“I find myself repeating myself and I certainly see myself here.
“I feel it's an answer that I've given so many times now but that very question is quite tiring.”