The Frenchman, who wore the iconic number seven jersey while at the club, scored 133 goals in 256 games, helping them to a Europa League trophy and a Champions League final among several title challenges.
He does have a €125 million release clause, which the suitors will be expected to activate, and that will give Atletico a chance to buy a potential replacement.
Here are three clubs with the financial ability and need to buy the 28-year-old.
3. Paris Saint-Germain
With striker Edinson Cavani on the wrong side of 30's, and decline evident with every passing game, PSG will certainly be evaluating their options this summer window. Should the Uruguayan accept a bench role or be sold, they will be on the look out for an elite striker, and Griezmann fits the bill perfectly.
The Frenchman has contacts within the club such as Kylian Mbappe and Presnel Kimpembe, who can potentially entice him into moving to Paris. While they have come under financial scrutiny lately, it doesn't seem like making a few sales and bringing Atletico's number 7 in would be a problem.
2. Real Madrid
Los Blancos are dreaming of signing a new world class number 9 to help Karim Benzema lead the line under Zinedine Zidane' in his second stint at the club. While there are constructive links to Frankfurt marksman Luka Jovic, a peek at the neighbours might not hurt.
Griezmann is experienced in the La Liga, still very much in his prime, and possesses a history of good connections with his strike partners. With Benzema and Griezmann at the fore, Madrid can truly make up for Cristiano Ronaldo's departure, as the new number 7 Mariano has struggled to make much progress at the club.
Barcelona have a history of purchasing world-class strikers at their prime such as Luis Suarez, Thierry Henry, David Villa etc., and Antoine Griezmann would fit right into that list.
With Suarez looking like he is past his prime, and Coutinho struggling to fit in at the club, despite spending 16 months at the Nou Camp, Barcelona should take the Frenchman's departure from the Rojiblancos seriously and snap him up as quickly as possible.
The €125 million fees can also be offset by reportedly outgoing players and therefore is a win-win scenario for the Catalan club. Barcelona have been linked to him in the past, and were the first club to be linked to him as he declared his departure.
3 potential destinations for Atletico Madrid star Antoine Griezmann