Despite missing out on the 29-year-old star, Wenger said he respected Vardy's decision.
"I think Leicester have made a statement and Vardy will stay. We were on the case and interested, but not more than that," Wenger told beIN SPORTS. "He has decided to stay at Leicester and good luck to him.
"He came late to the game and in fairness Leicester bought him from Fleetwood and he has been successful. He is 29 and he has chosen to stay at Leicester. You have to respect that."
Wenger, though, refused to rule out a move for Leicester midfielder and fellow Frenchman Kante.
After a spectacular season with Leicester, Kante has continued his red-hot form for France at Euro 2016.
"It is very difficult to talk about that at the moment," Wenger said. "Kante is on the list of many clubs. It is an area where we have many players.
"We will see what happens in the next two or three weeks. It looks like Leicester have bought a player from Nice [Nampalys Mendy] with similar qualities to Kante, so whether they envisage to lose him or not I don't know.
"If you ask 100 people in the street if they want Kante to play [for France] you will get 100 saying yes. He has done the job in one or two games and I am not surprised.
"I said two months ago this boy will play the whole European Championship. We know him well from Leicester now and I am not surprised that he is starting. He has been one of the revelations of the French team."