Arsene Wenger is out of contract at the end of the season
Wenger's future remains up in the air given the Frenchman's contract at Arsenal expires at the end of the season.
Arsenal on course to end a 13th consecutive campaign without winning the Premier League, with the Gunners trailing leaders Chelsea by 10 points.
Who could succeed Arsene Wenger at Arsenal?
Wed, February 8, 2017
Express Sport takes a look at top candidates who could replace Arsene Wenger at Arsenal
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Who are the favourites to replace Arsene Wenger at Arsenal?
But Keown, who was part of all three of Wenger's title-winning squads in 1998, 2002 and 2004, believes Arsenal's longest-serving manager will remain for at least one more campaign.
"My gut feeling is that he'll stay and then it's really how long he'll stay for," said Keown.
"I imagine he'll be given more time but I think maybe only one more season.
Martin Keown won three Premier League titles under Arsene Wenger
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"Then the club can row back from that if they need to. If he was to win the Champions League or the league they could look at extending it again.
"But to get everyone on board and for the fans to buy into it, it would be like a one season to go, one more season for Wenger, and it would give the great man the time he deserves."