The Gunners' failure to win a Premier League title since 2004 has led to some supporters calling for Wenger to end his reign at the Emirates, but the Frenchman revealed he will continue as long as he believes he can do a "good job".
Wenger, who was speaking ahead of Arsenal vs Chelsea, which is live on BT Sport on Saturday evening, told a live Facebook session: "I don't know (when I will retire) because I hope to never completely retire from football, because I still think when I watch a Premier League game on television I'm in football.
"I will not give you any name because I believe it would put the guy under big pressure. But, mainly because I'm pragmatic and I do not think it is my job to chose the next manager.
"My job is to perform for Arsenal and it's the board's responsibility to find the next manager. If they ask my opinion I would give it, but I wouldn't like to come out publicly."