The former Gunners defender says the club must start next season at 'boiling point' if they are to challenge for the Premier League title.
Arsene Wenger’s side have won 16 of their last 18 games in all competitions, a run which has seen them up to second in the Premier League table and into an FA Cup semi-final.
Keown, though, says their strong end to the season will ultimately be meaningless unless they can carry that type of form into next season, suggesting that the lack of a major tournament this summer will aid their cause.
“What they need to do now is try to have a complete season and start well,” he said.
“They need to begin the season at boiling point, not building up to it. Wenger tends to start better when there isn’t a major summer championship and they have a free summer.”
The former defender turned pundit has also suggested that rivals Chelsea will be under threat next season.
Jose Mourinho’s men have led the way throughout this Premier League campaign and look almost certain to win the title come the end of the season, although they were ultimately unsuccessful in the FA Cup and the Champions League.
Keown, though, isn’t getting ahead of himself after many thought Arsenal would be challenging this year following the summer signing of Alexis Sanchez.
“Next year you think Chelsea will be under threat,” he added.
“But we thought that last season, with Alexis Sanchez being the icing on the cake. It didn’t happen. It’s as much about mental strength as it is about performance.”