Lemar is now on global duty with France at the World Cup, and will link up with his new team-mates after the tournament once the deal is officially confirmed.
But after having previously stated that he would announce his decision before France's opening World Cup game on Saturday, Griezmann chose to keep shtum.
"Appearing alongside Griezmann, France coach Didier Deschamps joked that the player will be "staying in Spain" and teammate Kylian Mbappe said the only thing he knows that "[Griezmann] will be on the plane [to Russia]".
'Over the next days, both clubs will work to close the agreement for the definitive transfer'.
According to reports, the 22-year-old will sign a two-year contract with Atletico, as they look to build upon last season's Europa League triumph.
Deschamps prohibits players from undergoing negotiations during tournaments, which provides a further reason to believe that Griezmann's future will be public knowledge before France begin the competition.
However, at a France press conference on Tuesday afternoon, he declined to give an update on his future intentions.
"It's not the time or the place".
"Well No 1, he's made a decision", Balague told Sky Sports News.