The Manchester United defender has been on loan at Ewood Park since March, during which time he has played 12 times.
Rovers have lost just twice when Keane has featured, with the England Under 21 international chipping in with three goals as well as impressing at the back.
Bowyer would like to see Keane return to the club next season, but with the managerial situation at Old Trafford unresolved, Blackburn will have to be patient.
"The level of performances Michael has produced for us has been exceptional," Bowyer told the Lancashire Telegraph.
"But he's a Manchester United player and at the end of the season he's going to have to go back to Manchester United.
"So we'll have to see what the situation is there first and foremost."