The Gunners are 10 points behind Chelsea in the Premier League title race and face Bayern Munich in the last-32 of the Champions League.
Ian Wright met with Wenger last week and the former Arsenal striker claimed he was given the impression that he will leave in the summer.
And Keown has delved deeper into the debate over Wenger's future by suggesting the Arsenal boss should play a key role in selecting his successor.
Arsene Wenger's future as come under scrutiny in the past few weeks
Martin Keown wants Arsene Wenger to be involved in choosing his successor at when he leaves Arsenal
"The end has to come for everybody of course," Keown told talkSPORT. "I feel there is a solution to plan an exit.
"Maybe it is one year and he can row back if he wins the FA Cup, Premier League or Champions League.
"He needs to be a part of the decision. He knows who the top people are out there in Europe.
Keown insisted Wenger still has a job to do with Arsenal
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"We're talking like he's gone, of course he hasn't. There are big games to come.
"Bayern Munich this week. Go there and beat them, bring them back home and knock them out."
Wenger is yet to sign an extension to his Arsenal contract which expires in the summer.
But Keown believes that behind-the-scenes, Arsenal are clear about what their boss wants to do.
"I don't believe that the board don't know the direction Arsene Wenger is going (to take), it's a multimillion-pound business here," Keown added.
"It's about when do we announce it and present it to the fans. Wenger maybe wants to be able to prove (himself), to be seen he can do it on the football pitch."