Both clubs announced a "preliminary agreement" on a transfer, with Atletico saying the clubs will work together to complete the details.
However, at a France press conference on Tuesday afternoon, he declined to give an update on his future intentions.
France begin their World Cup campaign against Australia June 16, before facing Peru (June 21) and Denmark (June 26).
Lemar is now on worldwide 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.
He made his France debut in 2016 and has scored three goals in 12 worldwide games.
France won the 1998 World Cup on home soil in a memorable tournament.
Should he make the switch, Griezmann would add further star power to an attack that already includes Messi, Luis Suarez and Ousmane Dembele. But I'm not going to speak about it today.
The duo are being interviewed at the same time, reeling off names of their favourite players as the presenter says: 'They are so cute we can not refuse them anything'.
Puig officially extended his contract with Barcelona and now has a release clause of €100 million, which should fend off any potential suitors for a while.
However, those figures will return to the previous numbers next month.
Lionel Messi believes his signing would go a long way in helping Barcelona become European champions for the first time since 2015.
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