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.
'The two clubs will continue to work in the coming days in order to find a definitive agreement'.
France travel to the World Cup on the back of a surprising 1-1 draw with the US in Lyon on Saturday night, but Griezmann reckons there's no need for his teammates to panic, and says their preparation for Australia starts now.
The winger is rated at around £65m but Arsenal did bid £90m on transfer deadline day last summer as they looked to push through a late deal.
There appears to be no logical reason behind Griezmann delaying the announcement of a new deal, if he is to stay at Atletico, and it would now be more surprising if the forward doesn't switch clubs this summer.
But those closest to the 27-year-old are urging him to stay at Atletico, sources said, with one source indicating there is no sign at this time that Griezmann is planning on a move to Barcelona.
Griezmann insists he is made a decision on his club future but has refused to reveal if he will remain with Atletico next season.
France play their opening game of the tournament on Saturday against Australia. "Yes I have already made a decision about my future".