Reports in Spain had suggested Atletico would look to move on Griezmann this summer -- he's on a two-year loan from Barcelona which will become an obligatory purchase if he plays a set number of games next year -- to ease the pressure on their wage bill.
High earners Alvaro Morata and Saul Niguez are both due to return for preseason training next month with their loan spells ending at Juventus and Chelsea respectively, while the lack of salary cap space means the club haven't yet been able to make official the free transfer arrival of Axel Witsel.
Multiple sources told ESPN that while Atletico were looking at ways of trimming the squad to resolve the situation, Griezmann would not be leaving this summer.
The long-term future of Morata -- who spent the last two years at Juventus, with the Serie A side unwilling to pay the agreed €35 million fee to make the move permanent this month -- is less clear.
Atletico president Enrique Cerezo confirmed this week that the club have to bring in €40m in player sales before they are able to make any more signings this summer.
Following the deal for Witsel, 33, who joins to cover the departure of Hector Herrera, the club would like to sign a first-choice right-back having been unconvinced by their options since Kieran Trippier left for Newcastle in January.
Griezmann, 31, endured a difficult season in front of goal last year, scoring just three times in LaLiga -- the worst tally of his professional career -- in 26 appearances.
In May, Griezmann told ESPN he was "pissed and annoyed" by his lack of goals as Atletico battled to qualify for the Champions League.
That followed a disappointing two years at Barcelona, who he joined from Atletico in a controversial €120m move in the summer of 2019.
He had previously spent five successful years at Atletico, becoming the fourth-highest scorer in the club's history.