Didier Deschamps left many top stars out of his World Cup squad but kept faith with Lemar, who scored recently for France in a win over Colombia and bagged a brace previous year against the Dutch.
It was no secret that Atletico had been looking for attacking reinforcements, as the club reluctantly sold both Yannick Carrasco and Nicolas Gaitan to Chinese Super League side Dalian Yifang in February, well after the transfer window had closed in LaLiga.
"The two clubs will continue to work in the coming days in order to find a definitive agreement".
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Sources told ESPN FC that Atletico star Antoine Griezmann worked actively to bring Lemar to the club and is excited to play with him.
But instead Griezmann wanted only to talk about his and France's preparations for their opening game of the World Cup against Australia on Saturday.
The MEN still holds out hope that Griezmann could move to Old Trafford next season, citing reports in the Spanish press last week that "claimed the 27-year-old is closer to a move to United than he is to Barcelona". "The decision will be made at the right time".
Lemar, who joined Monaco from Caen in 2015, was a key player for the principality club when they reached the Champions League semifinals in the 2016-17 season.
He made his France debut in 2016 and has scored three goals in 12 worldwide games.