The Daily Star says Mackay is poised to sign a three-year contract to replace Tony Pulis at Selhurst Park.
The former Cardiff boss has been promised "significant funds" to spend before the end of the transfer window.
Mackay has been out of work since he left Cardiff last December but has beaten off strong competition for the job.
Former Tottenham boss Tim Sherwood was a strong contender, while Glenn Hoddle also emerged as a late candidate.
But Mackay is close friends with Palace sporting director Iain Moody from their time together at Cardiff and that helped strengthen his case.
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