The 20-year-old, signed from FC Copenhagen for £8.5 million this summer, was the Bluebirds' record signing until they purchased Steven Caulker from Tottenham.
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"Andreas joined in with training last Friday but wasn't match fit. He took an ankle knock in training two weeks ago and was nearly ready," Mackay told the press.
"If he damaged the ankle again he could have been out for four weeks. We're looking at the long-term picture and that's why we've waited another week.
"We are making sure he's OK. He'll be back in training this week and should be in the squad to face Manchester City."
The Danish striker has scored 18 times in 34 matches in his short career to date.