Reports in Italy have suggested that Carlo Ancelotti would be interested in the job following his sacking by Bayern Munich, although the three-time Champions League-winning manager would likely have to wait until at least 2019, when Wenger's current deal expires.
Ancelotti has already ruled out a return to management this season, but Wenger was keen to stay out of the debate as to whether the 58-year-old would be a possible replacement at the Emirates Stadium.
"I don't know who will replace me at Arsenal. When you're a manager for a club you have to work like you're there forever," he told beIN Sports.
"It demands total commitment. I believe as well that the football club works by everybody doing his own job well. My job is to prepare the team for the next game and be responsible for the technical policy of Arsenal Football Club.
"The job of my board is to choose the next manager. I don't want to do the job of the board."
Ancelotti has previous experience of the Premier League with Chelsea, where he won the double in his first season.