The former Gunners centre-back believes Varane is good enough to make a difference at Old Trafford as he is 'the best young centre-back out there.'
"I’m a big fan of Raphael Varane at Real Madrid and would probably have a look at him," Keown said as part of his 'Tackle Keown' Q + A on the Daily Mail's website.
"He is the best young centre back out there but still has room to improve and perhaps another young defender is not what United need.
"He would be difficult to prise out of Madrid but if he’s not playing because of the form of Pepe and Sergio Ramos, then maybe he might want to play.
"On the other hand, if he is the future for Madrid then perhaps Pepe or Ramos could be convinced to move on. Ramos in particular would be an excellent addition."
By comparison, Keown is of the opinion that, despite stating Chris Smalling's potential, none of the current Manchester United defenders would make it into one of Sir Alex Ferguson's 'great teams.'
"If you look at them as individuals, I don’t think any of them would come close to getting into any of Fergie’s great teams and would probably struggle to make it into the squad," he added.