Vlaar has been linked with a number of Premier League clubs in the wake of an impressive World Cup this summer, but Keown believes the 29-year-old is not suited to Arsenal.
"If I'm going to be picky, I don't think he's mobile enough," Keown said in the Daily Mail. "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 reported to have begun fresh contract talks at Villa Park.