The former Arsenal defender is disappointed with the young midfielder, who has made a bad name for himself time after time.
The 23-year-old was recently pictured with a shisha pipe, adding to previous incidents where he has - for instance - been caught smoking and showing a middle finger to fans while on the field of play.
And Keown is disappointed with the Arsenal's star's repeated lack of professionalism. Indeed, he has urged the young Gunner to sharpen up - and wants someone to teach him how to do so.
"Surely it’s time to start educating Jack and have somebody explain to him how to behave," Keown said during a 'Tackle Keown' session.
"If he was smoking that pipe, even if it doesn’t do him any serious damage, as a player I wouldn’t put myself in that position.
"You have to be squeaky clean and, if you are serious about your football, that’s how you should want to live anyway."
Wilshere has been out of the Gunners' side through injury for most of the current season and, considering his evident lack of decision-making ability off the field - combined with the form of his Arsenal team-mates - it is difficult to see him ever forcing his way into Arsene Wenger's starting XI as a starter every week.
When fit, however, Wilshere hasn't failed to deliver, shining on occasion this term.
But it appears the 23-year-old's injury record isn't the only thing holding him back. Keown is right - what on Earth is the young Arsenal man playing at?