The former Gunners centre-back was asked whether the Dutchman would suit a move to north London, or perhaps even Manchester, but Keown believes he isn't mobile enough.
The Arsenal legend did, however, admit Vlaar is a good defender - but he feels a club like Arsenal need an upgrade on their current centre-backs if they are to bring anyone in, something the 29-year-old isn't.
"If I’m going to be picky, I don’t think he’s mobile enough," Keown wrote as part of his 'Tackle Keown' Q + A on the Daily Mail's website.
"He played well at the World Cup for Holland as part of a back three but that was because he had quick players either side of him.
"He’s a solid player but before somebody like Arsenal or United go in for him it’s important not to think of Vlaar the World Cup player but remember Vlaar Villa player last year.
"He is a good defender and obviously Villa won’t want to lose him but it’s different when you’re buying a player. You want them to improve on what you already have and I’m not sure he would at United or Arsenal."
Vlaar is reportedly in contract talks with Aston Villa anyway, although both Arsenal and United are in desperate need of defensive cover at the moment.