The north London side suffered a damaging blow to their title hopes last weekend when they were beaten 3-1 by the Blues at Stamford Bridge to leave them 12 points behind the leaders after 24 games.
Manager Arsene Wenger has told Arsenal fans to be more united behind the team like Tottenham supporters.
"If Wenger were to lose this I think it would seriously question whether he should stay on", said Keown.
That said, there still exists plenty of quality, high-end options to take over for Wenger, and while the task appears a daunting one, life after Arsene can be successful if the right man is put in place. We are in a pack that is very tight, where the fight for every position will be massive. It's not me at stake, it's Arsenal Football Club and Arsenal's season at stake. Use the filter system to refine which games you should bet on and view the analysis that mathematical system produces to give you the best chance of making money from the Arsenal vs Hull game.
Wenger's men take on Hull City at the Emirates this Saturday, and it could be a potential banana skin as Marco Silva's side recently defeated Liverpool and held Manchester United to a draw.
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It's not the first time he's been dropped. "But he is 19 years old, Brazilian, physically strong, he needs few training sessions to be ready".
"What is important for me is that Arsenal Football Club does well, and I dedicate my whole energy to the club doing well - I am a professional and I have to do a job and that's what I want to do".
"This is an important and very sensitive part of the season and we have to respond to disappointment together", said Wenger, who has midfielder Mohamed Elneny available again after worldwide duty.
"Ideally you want everybody to be happy", he said when asked what would influence his decision on whether to sign a new contract. We fight with teams who invest much more than we have and we have to stick together and respond.
The Frenchman called for fans to back the team ahead of a crucial run of fixtures - in a similar way to their bitter rivals Tottenham.
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