Griezmann, 26, has been heavily linked with Manchester United in recent months.
He talked up a possible move to Old Trafford on French TV only last week.
The forward said the likelihood of him joining the Red Devils was "six out of ten".
However, according to Don Balon, Ateltico are not planning to let Griezmann leave the Spanish capital anytime soon.
Instead, they have reportedly tabled a lucrative new contract for the France international, who scored 26 goals in all competitions this season.
It would apparently make him the highest-paid player in the their history, while also including the promise that they will fight for major titles.
Atletico are set to move into their new 70,000-seater Wanda Metropolitano stadium this summer.
And the club are sad to consider Griezmann an "essential" part of their future.
Atletico president Enrique Cerezo ruled out an exit for his star man this weekend.
He told Marca: "Griezmann will stay here. Not here at the Calderon, but at the Wanda."
