Palace withdrew a firm offer of employment after Bluebirds owner Vincent Tan sent the document to the governing body, according to The Mirror.
The papers are said to call into question the level of fees, commission and role of agents in several transfers during Mackay's two years in charge at the Welsh club.
Evidence of racist, sexist, and hompohobic texts and emails is also rumoured to be outlined in the document, allegations that the FA could now investigate.
Palace director of football Iain Moody, who worked alongside Mackay at Cardiff, is also said to have been named in the dossier.
Mackay left Cardiff amid a firestorm of controversy following a bitter falling out with Tan that resulted in him suing the club for £7.5m, only to later withdraw the lawsuit.