Keown, speaking at BT London Live in Hyde Park, is confident the club have learned from past mistakes and will move quickly to ensure that the van Persie situation is resolved as soon as possible and a suitable replacement is found.
"At least van Persie has come out early and declared that he wants to leave," Keown told the London Evening Standard.
"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. 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 centre back, who won three league titles with the Gunners, said that the club must invest in at least one world class talent and stem the flow of quality players leaving the club to show that Arsenal are progressing in the right direction.
"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."