Manchester United have been linked with the Burnley defender but Keown is worried he may struggle for game time at Old Trafford.
The defender has excelled since signing for Burnley and the Clarets would be loath to let him go, but with the BBC claiming United want to bring the player back to Old Trafford, Keown hopes that he actually gets regular game time.
"I just hope that United are signing him for the right reasons," Keown wrote. "If he is not going to play next season then he should be allowed to continue to flourish at Burnley.
"I am concerned with the level of competition he would face at United from the likes of Chris Smalling, Eric Bailly and Phil Jones."
When you also factor in Marcos Rojo and Daley Blind, it is clear that when United have all their defenders fit and firing there is a lot to choose from.
That said, United manager Jose Mourinho will know he needs to find the right long-term partner for Bailly and Keane could be the answer.
Rojo was in superb form prior to his season-ending injury but doubts remain over whether Jones, Smalling and Blind can be regarded as the elite class of defender United need to challenge at the top table next season and beyond.
If he fulfils his potential Keane could form the bedrock of United's defence for the next decade, and that would be well worth the sizable outlay required to bring him back.