The 42-year-old has been out of work since parting company with the Bluebirds in December last year.
"[Mackay] is still young in management terms and has done very well in his career so far," Cowie told the Daily Mail. "I'm sure he is desperate to get back in quickly. The Celtic job would probably suit him perfectly. He is available and I can see no reason why he is not the man for it."
Mackay spent five years at Celtic during his playing career.