Griezmann is set to announce his intentions before France begin their World Cup campaign against Australia next Saturday.
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.
"We understand there won't be easy matches at the World Cup for us", the Atletico Madrid star told French sports daily L'Equipe.
While Manchester United have been linked with Griezmann previously, Deschamps said the forward was staying in Spain.
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Griezmann said earlier on Tuesday that he had made up his decision on his future but would not reveal his plans, though sources have since said all signs point to him returning to Atletico. But I'm not going to speak about it today.
"I know there's a lot of expectation, I know many were waiting for it, but today is not the day (to speak about my future)". The deal, should he sign, will make him the club's highest paid player; and the entire club has been endorsing the deal since it was offered - from the president right down to the kit man. And Griezmann is one of them.
After facing the US on Saturday in Lyon, France are due to fly to their training base near Moscow on Sunday.
"Cristiano Ronaldo leaving, out of 10, I'm anxious about a five or a four", he said.