Mackay and Moody, former manager and head of recruitment respectively at the Welsh club, are the subject of a dossier submitted by Cardiff following months of disagreements and legal wranglings.
And the FA told Perform on Thursday that they have launched a probe after receiving the document.
"The FA can confirm it is currently investigating this matter," said an FA spokesperson.
Cardiff owner Vincent Tan oversaw the exits of both Moody and Mackay late in 2013, with Moody going on to join then-Premier League rivals Crystal Palace before resigning from his position on Thursday.
Following allegations of spying from Cardiff prior to a top-flight fixture against Palace, the London club were fined by the Premier League for their part in the matter.
In recent days, the saga took another turn when Mackay's apparent chances of taking over from Tony Pulis at Palace ended due to potential legal action from Cardiff against the Selhurst Park outfit.
Mackay had dropped his claim for wrongful dismissal and apologised to Tan in May after the Malaysian businessman came under much criticism for replacing the Scot with Ole Gunnar Solskjaer.
Cardiff were duly relegated to the Championship with Solskjaer at the helm.
