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Monday's 3-0 defeat by Crystal Palace left Arsenal in sixth place, seven points adrift of fourth-placed Manchester City with eight games left.
Wenger, whose deal ends this summer, has led Arsenal to top-four finishes in each of his 20 seasons in charge.
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On the top four, he said: "We might get there, we might not get there."
The Frenchman has been offered a new two-year deal, although he is yet to announce whether he will continue.
Five defeats in their past 10 Premier League games have prompted some Arsenal fans to call for Wenger to leave the club.
Asked on Friday about his future, Wenger said: "What is happening at board level is not down to me.
"I focus on what is down to me, the performance of the team and what the fans are interested in is the performance of the team."
The Gunners are at struggling Middlesbrough on Monday (20:00 BST).
Wenger refused to comments on reports forward Alexis Sanchez had been offered a new £300,000-a-week deal.
The Chile international, 28, who is contracted to the Gunners until the summer of 2018, was nominated for PFA Player of the Year award this week after scoring 18 goals and assisting nine in the league this season.
"I'm very happy because it rewards a very strong season if you look at his numbers," added Wenger.
"He basically prefers to play wide rather than up front because he can get the ball more. He has to keep that balance between providing and goalscoring because he has both in the locker."
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Arsenal face a "massive" challenge to qualify for the Champions League, says boss Arsene Wenger, who added "nothing" has changed about his future.