It was expected the forward would leave the Wanda Metropolitano during the current transfer window after almost leaving a year ago.
Back then the France international was close to moving to Manchester United, while this time around Barcelona have expressed an interest too.
But, according to ABC in Spain, Griezmann is staying put at Atletico Madrid this summer.
The report claims the 27-year-old has told close friends that he will not be leaving as he is happy at the club.
Atletico, for their part, are said to be delighted by the news and will reward Griezmann with a new contract.