The 20-year-old's current stay is due to expire after the Rams' clash with Yeovil on Tuesday.
"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.
"I hope that Michael can see he will get games here, that his development will carry on at a good level.
"I think it (centre-back) is an area in which we have to look if we lose Michael.
"Hopefully, we can keep him."
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