The Dutchman recently expressed his intention not to sign a new contract and looks set to join the likes of Cesc Fabregas and Samir Nasri as the next high profile name to leave north London.
And Keown, who enjoyed a distinguished trophy-laden spell with the Gunners, hopes to see Van Persie's future sorted as soon as possible to avoid speculation damaging the club's chances for the new season.
Keown told talkSPORT: “At least Van Persie has come out early and declared that he wants to leave.
"Last year when it was Nasri and Fabregas it impacted so much on the group that when they were seven games in it was like a relegation fight.
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“And I think this round this won’t happen if van Persie goes. I think the squad is stronger both mentally and in quality."
The former England stopper also believes that Wenger must look to sign a player of similar calibre to Gunners legend Dennis Bergkamp in order to move forward.
Keown added: “We’re almost kind of getting used to losing top players now, it’s just a shame that so many are going.
"If we look back to Dennis Bergkamp coming to the club, when he came to the club, it was kind of like ‘Christ!’ That was a real wake-up call - he came in, everyone took note, Arsenal’s going in a different direction.
“Arsenal could almost do with one of those world stars coming in again."