Griezmann was close to closing a move to Barça after months of talks once his release clause dropped to 100 million euros on July 1.
It is understood that representatives of Monaco and Atletico met on Tuesday evening to discuss the transfer, with Lemar now involved with the French national team at the World Cup in Russian Federation, as reported by French news outlet L'Equipe.
France kick off their World Cup campaign against Australia on Saturday and Griezmann had previously insisted that he would reveal his future before that match.
France coach Didier Deschamps prohibits players from undergoing negotiations during tournaments, pushing Griezmann towards making a decision.
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"I'm sorry for the wait, but today is not the day".
Of course, if he was staying at Atleti, why wouldn't he just come out and say it now if he's already made his decision?
Griezmann has scored 112 goals and assisted a further 40 strikes in 209 games for Atletico since his arrival at the Vicente Calderon in 2014.
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Most of the Catalan's squad have commented on rumours that the star could move to the Nou Camp.
Monaco today confirmed that they have agreed a deal in principle with Atlético Madrid for the sale of Thomas Lemar.
Dermot Corrigan is a Madrid-based football writer who covers La Liga and the Spain national team for ESPN FC.
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