The 20-year-old is on loan from Manchester United, with his current stay due to expire after the Rams' clash with Yeovil on Tuesday.
However, the former England manager is keen to extend Keane's spell in the east Midlands, but admitted it is out of his hands.
"We have got him to the Yeovil game and then it is up to Manchester United and himself to make the decision," McClaren told the Derby Telegraph.
"But we definitely want to keep him to the end of the season."
Keane did lose his place in the side after captain Richard Keogh returned from injury, and McClaren admits he needs cover for his skipper.
"I hope that Michael can see he will get games here, that his development will carry on at a good level," said McClaren.
"I think it (centre-back) is an area in which we have to look if we lose Michael."