The Gunners have been linked with the France international all summer long and are thought to have had numerous bids rejected, each falling short of the Ligue 1 champions' supposed £50m valuation.
Recent reports suggested that Arsenal would return with one more offer before the transfer window closed, but Wenger has all but ruled out landing Lemar due to the ongoing uncertainty surrounding the futures of Kylian Mbappe and Fabinho.
"It's dead because Monaco have closed the door, definitely," he told reporters. "They're still on cases like Mbappe and Fabinho. They've already lost [Benjamin] Mendy, Bernardo Silva and [Tiemoue] Bakayoko, so Monaco is at a stage where they have closed the door."