Both clubs announced a "preliminary agreement" on a transfer, with Atletico saying the clubs will work together to complete the details.
They claim that Griezmann has chose to join Barcelona.
North Korea: Trump has agreed to step-by-step denuclearization
Many said they welcomed the USA and North Korea moving to narrow their differences, but remained cautious and skeptical. Others think the agreement is in some ways a step back compared to past negotiations.
A source close to the deal told AFP the transfer fee would be around €75 million, with the Guadeloupe-born player's contract running out in 2020.
Having become an established part of the first team in 2015-16, Lemar kicked on further, turning out 34 times in the French top flight and returning nine goals and 11 assists.
Atletico Madrid are clearly convinced by Lemar's vast talent, and, should he continue to improve, he should prove an intelligent purchase. In fact he played 35 games for Monaco, showing his best form at the latter end of the season.
Justify wins Belmont Stakes to become 13th Triple Crown champ
It had previously won the Kentucky Derby and the Preakness Stakes , which together make up horse racing's most sought-after title. Bob Baffert and Mike Smith have teamed up to win a big race at Belmont Park . "I told him I loved him", he said.
Antoine Griezmann says he has made a decision on his future but refused to clarify where he will play next season when he spoke to reporters at France's World Cup camp in Russian Federation on Tuesday.
"He promised that everything would be sorted before the World Cup, it's not going to be the case".
Monaco's exploits saw Bernardo Silva, Benjamin Mendy and Tiemoué Bakayoko among those to move on last summer, while Kylian Mbappe moved to PSG on loan with a view to a permanent move.
Xi touts Putin ties as USA tensions brings them closer
Special prosecutor Robert Mueller is investigating Russia's involvement in the election, including links to Trump's campaign. Shortly before arriving at the summit in Canada Mr Trump said: " Russia should be in the meeting, should be a part of it".
Now it is Griezmann signing the autographs and carrying the hopes of a nation on his shoulders.