Lemar is a part of Didier Deschamps' France squad in Russian Federation and could be in line for a start in their first game against Australia on Saturday should Kylian Mbappe miss out with an ankle knock.
But he told a news conference: "I apologise - I am really very sorry".
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But Griezmann has remained tight-lipped on his decision, refusing to reveal his future destination just yet. I have made my choice.
But he finally appears to have secured his next challenge, with Atletico giving every indication they want to close the gap on LaLiga champions Barcelona next season by signing a highly rated attacker.
France play their opening game of the tournament on Saturday against Australia.More news: Robbie Williams set for World Cup opening ceremony
While Manchester United have been linked with Griezmann previously, Deschamps said the forward was staying in Spain.
Barca's pursuit has angered Atletico, who in December reported them to Federation Internationale de Football Association for making an alleged illegal approach and followed up with a statement in May that said "enough is enough".
Puig is one of the most talented footballers of the younger generation and has been deemed to step into Lionel Messi's boots at the Camp Nou when the Argentine talisman steps down from the club.More news: Some lava evacuees in Hawaii may return to homes during 'stable' flow
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