Griezmann, 27, continues to be linked with a move to LaLiga champions Barcelona after another fine season at Atletico.
"The World Cup for France starts on Saturday, there is still time".
The Atletico Madrid forward was expected to announce his summer switch to the Catalan outfit during a press conference on Tuesday.
However, despite suggestions he will choose Atletico, still Griezmann declined to say either way what he plans to do when the subject was raised by the gathered media.
But Griezmann has remained tight-lipped on his decision, refusing to reveal his future destination just yet.
"I know that many of you were waiting for that. However, today is not the day for that".
Puig officially extended his contract with Barcelona and now has a release clause of €100 million, which should fend off any potential suitors for a while.
Griezmann had hinted that he would sort out his future before the World Cup, but now it looks like fans will have to wait until afterwards to find out what he has decided.
Seeing how things have come full circle for Griezmann is just lovely and we're eager to see how he performs on the grandest stage of them all, especially considering how electric he was two years back. However, Atletico responded with a counter-offer which will make him the club's best paid player by some distance.
So despite the temptation to play with Lionel Messi at Barcelona, most signs point to Griezmann staying put.