The Football Association is looking into allegations made by Cardiff against former manager Malky Mackay and Moody, who worked at Cardiff before moving to Crystal Palace..
Mackay's name was dramatically pulled from the race to take over from Tony Pulis as Crystal Palace manager on Wednesday just before the existence of the dossier became public knowledge.
A statement from Palace read: "In light of the events of yesterday, sporting director Iain Moody has tendered his resignation and it has been accepted with immediate effect. There will be no further comment from the club on this matter."
Sky Sports understands the dossier was sent to the FA more than a week ago and the governing body has now confirmed it is investigating the matter.
It reportedly includes allegations against Mackay and Moody from their time together in Cardiff.
The allegations refer to work-related text messages sent between Mackay and Moody that bring the game into disrepute. Those messages are believed to be homophobic, racist and allegedly sexist.
An FA spokesman said: "The FA can confirm it is currently investigating this matter."
League Managers' Association chief executive Richard Bevan confirmed to Sky Sports the body's lawyers are going through the allegations and will respond in due course.
Cardiff owner Vincent Tan sacked Mackay in December 2013, just six months after he had ended the club’s' 51-year wait for top-flight football.
Two months earlier Moody had been placed on gardening leave by Tan before being subsequently dismissed.
Mackay launched a £7.5m legal claim against Tan for compensation and wrongful dismissal after his sacking but dropped the claim in May and issued an apology to the Malaysian businessman.
With Mackay apparently out of the race, former Tottenham manager Tim Sherwood is now the favourite to take over from Pulis at Selhurst Park.