The Gunners made three bids previously for Lemar, the highest of £50m, which were all rejected by the Ligue 1 champions.
However, Lemar opted against a last-minute move to Arsenal with some reports suggesting the France starlet was holding out for a move to Liverpool.More news: Seahawks trade Jermaine Kearse to NY Jets for DE Richardson
Wenger said: 'It's dead because Monaco has closed the door.
"You do not want to talk too much about. you have to respect what happens on the negotiation side".
Lemar's preference was Liverpool, but the Reds were unwilling to bid above their valuation of £65m, resulting in the forward staying at Monaco for another year.More news: Chief Minister Captain Amarinder Singh
"I am a player of Monaco, I am very happy there", Lemar, who joined from Caen for less than €4m in 2015, told Canal+.
Lemar was one of the most coveted players throughout Europe heading into Thursday's deadline day, with Arsenal, Liverpool and Barcelona all considering moves for the winger.
Lemar, the A.S. Monaco midfielder, has been a target for Jurgen Klopp's team in the final weeks of the window, as Liverpool completes a late spree of spending.More news: Trump says Missouri Sen. McCaskill should back tax cuts or lose re-election
The Belgian worldwide Origi has managed 12 Premier League goals from two full seasons with the Merseyside club and they are said to be willing to let him go.