The Gunners faithful were vociferous in their desire for the right-back to sign a new contract during Sunday's 1-0 win over West Brom, with the 31-year-old's current contract deal to expire at the end of the season.
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"I want him to stay," he said at the post-match press conference. "There are two players at the end of their contracts, Sagna and [Lukasz] Fabianski. If it's down to me, they both stay."
Asked if it might have been his final home game in charge of the club, Wenger replied adamantly: "No, no. Don't be impatient; my last game will come. Don't worry.
"Yes, [I will be here next season]. I have told you many times, my word is my word," he added, also noting that his delay in signing a new contract had nothing to do with waiting until after the FA Cup final.
With Arsenal's top-four place guaranteed before the game, Wenger reflected on the failure of their challenge for the Premier League title.
"I am happy with the attitude, behaviour and consistency of my players and frustrated, as well, because we had 120 days at the top of the league. When you look at it today, it's very tight - and then it comes into your mind, the points you dropped," he said.
"We had injuries - three or four players who missed too many games - and, in some games, at the start away from home, we were caught by surprise. We were perhaps too cautious and not confident enough. We paid a heavy price for it."