The Daily Mail has reported that the document contains allegations of racist, sexist and homophobic text messages and Mackay now looks to be out of the running to succeed Tony Pulis at Crystal Palace.
Press Association Sport understands the dossier was filed over a week ago and was not deliberately timed to have any effect on Mackay's candidacy for the Selhurst Park vacancy.
FA sources confirmed receipt of the dossier.
Cardiff owner Vincent Tan sacked Mackay in December 2013, just a few months after the Scot had ended the Bluebirds' 51-year wait for top-flight football.
Two months earlier Moody, Cardiff's former head of recruitment and now Palace director of football, had been placed on gardening leave before being subsequently dismissed.
Mackay launched a £7.5million legal claim against Tan for compensation and wrongful dismissal after his sacking but suddenly dropped the claim in May and issued an apology to the Malaysian businessman.
Cardiff have declined to make any public comment on the dossier and the matter is now in the hands of the FA.
Earlier this week Palace were fined by the Premier League for their part in the 'spygate' saga involving Cardiff last April.
The Premier League determined that Palace had breached its 'good faith' rule - B16 - by obtaining information about Cardiff's team ahead of their 3-0 win when the two clubs were relegation rivals.
The Welsh club had complained to the Premier League that Moody had contacted Cardiff employees for information in the build-up to the game, an accusation Moody denied.
Source : PA
Source: PA