The Gunners boss has continuously refused to reveal whether he will sign a new contract to extend his stay at Emirates Stadium beyond this season.
Wenger again did not give an indication over his future plans prior to the final at Wembley on Saturday, even though he insists the result will have no bearing on his decision.
Asked if his Arsenal reign would extend from 21 years to 22 or 23, Wenger said: "I cannot answer that question at the moment.
"It will not be my last match anyway because no matter what happens I will stay in football."
Asked specifically if this would be his last match in charge of Arsenal, he replied: "I don't know.
"No [the result will not have an impact]. Why [should it]? I don't care about me, I care about us winning the game on Saturday.
"When you go in the game, a cup final, you can accept the challenge and just want to win it. The last worry I have is myself.
"The team has given so much and they really want to win something this season."
Wenger insisted he has not thought about going out on a high if Arsenal are able to beat rivals Chelsea and secure FA Cup glory.
"No, what I want is to win the next game," he said. "I love to win and I want to do well for my club. I want to win the cup for my club and that is all I care about.
"It is not about me, it is about us winning the trophy and giving absolutely everything to achieve it."