Goal reported in June that Arsenal launched a €35m (£30.7m) bid for Lemar but the offer was swiftly rejected by Monaco.
And now Wenger has revealed that negotiations between the two clubs are over.
“It’s dead because Monaco I think has closed the door definitely,” said the Frenchman.
“They’re still on cases like Kylian Mbappe and Fabinho. They have already lost Benjamin Mendy, Bernardo Silva and Tiemoue Bakayoko.
“Monaco is at a stage where they’ve closed the door. We have the numbers and quality to deal with that.”
Despite missing out on Lemar, Wenger insists he is “very happy” with Arsenal's squad as they look to reclaim a place in the Champions League.
The north Londoners have signed both Sead Kolasinac and Alexandre Lacazette so far this summer and Wenger says the club currently have “too many” players on the books.
Wenger added: “I’m very happy with the strength of our squad. I’ve said many times before we have too many players in our squad.
“Some of them will have no chance to compete for places because we have too many. On the other hand, one of the values of this club is to give chances to young players.”