Monaco winger Lemar has been a target for Wenger all summer but the Gunners have struggled to land a deal.
Reports in France earlier this week suggested the Ligue 1 champions were open to cutting a late deal.
But Wenger claims Monaco have no intention of selling the winger.
Speaking at a press conference this morning, he said: “It’s dead because Monaco have closed the door definitely.
"They are still on cases like Mbappe and Fabinho.
"They’ve already lost Mendy, Bernardo Silva and Bakayoko, so Monaco is at a stage where they have closed the door."
Lemar emerged as one of Europe's hottest talents last term, providing 14 goals and 17 assists in 55 appearances.
Arsenal have a number of fringe players to offload before the window slams shut next week.
But Wenger is still hoping to bring in new signings and he said: “Both (ins and outs) can happen in the last seven days.”
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He added: “I am completely happy with the strength of the squad. I have said already we have too many players. Some players have no chance to play.
“If you have too many players of confirmed status you are in a difficult position to give a chance to young players.”
Arsenal travel to Liverpool on Sunday and Alexis Sanchez is fit to play.
