In his press conference before Arsenal take on Chelsea at Stamford Bridge on Sunday, Wenger admitted he was interested in signing Costa. The Arsenal boss was heavily linked with several strikers over the summer, including Mario Balotelli and Karim Benzema, but eventually signed Danny Welbeck from Manchester United on deadline day.
Wenger on Welbeck
Wenger press conference
When asked if he tried to sign Costa, Wenger said: "Yes, but that deal [Chelsea] was a deal that was struck early."
The Arsenal manager was full of praise for the new Stamford Bridge forward, who has quickly settled into Premier League life. The goal against Aston Villa last weekend was Costa's eight of the season already.
Wenger hailed the striker as a 'killer' although he admitted that he's been surprised by how swiftly Costa has adapted.
"Costa has done fantastically well, I must say," Wenger continued. "I am impressed by how well he has done.
"He has all the aspects of a striker that I like. He is focused, always determined and ready for a fight. He has players like Cesc who can always find him. He is a very efficient player, the timing of his runs and killer determination.
"You feel this guy is a killer and he has that in him."
The 25-year-old former-Atletico Madrid star was never tipped to join Arsenal over the summer even though it was well documented that Wenger was looking for competition for Olivier Giroud.
Chelsea were always the frontrunners, and they raided Atletico again to sign Filipe Luis as well.
Wenger meanwhile focused his attention first on Alexis Sanchez, signing the ex-Barcelona star off the back of a fantastic World Cup, and he took the opportunity to sign Welbeck after he was deemed surplus to requirements by Louis van Gaal following Manchester United's deal for Radamel Falcao.