Sir Chips Keswick retired from the position last week, after spending 15 years on the board.
Keswick admitted he always wanted to leave, but the COVID-19 pandemic has made him bring his decision forward.
The Gunners are now looking for Keswick’s successor and Keown insists Arsenal should look no further than Wenger.
“It would be something special to see Arsene Wenger come onto the board.
“I don’t think so somehow, I think he’s said recently he doesn’t want to do that, never saw himself as someone who would sit on the board but they could do a lot worse.
“You know that I feel that would be almost the perfect answer for Kroenke, the young Josh Kroenke, he needs that older person perhaps around, someone with the experience,” Keown told talkSPORT.