It was thought that Griezmann would complete a €100m move to Camp Nou this summer, with Barça tipped to trigger his buyout clause and the player expected to jump at the opportunity.
However, the once 'imminent' deal has been hit by increasing doubt in recent weeks.
Just this week, Griezmann himself told German outlet Spox, "I'm thinking about it; I still haven't decided." That is despite previously expressing hope that his future would be sorted before the World Cup kicks off, which is only just over a week away.
According to Spanish network Cope, Atletico will pay Griezmann big money to remain at the new Wanda Metropolitano this summer. It is said the club will offer a net salary of €23m per year and is even 'optimistic' that he will sign a fresh deal instead of leaving.
Had Griezmann been certain of wanting to join Barcelona it is likely the saga would already have been resolved. The longer it drags on, the more it seems to favour Atletico instead.
Griezmann has scored 112 goals in 209 appearances for Atletico since his €30m arrival in 2014.
His and France's World Cup campaign will begin when Les Bleus face Australia on 16th June.