John Foley was due to take over the role this morning but has now decided against taking up his appointment.
In a statement this morning, the board of the association said it noted Mr Foley’s decision “with great regret.”
“Throughout our dealings with John, his suitability for the role was beyond question and the level of professionalism and clarity he could bring to the Association would have been invaluable.
“John’s experience and influence will be especially missed by our staff, who would have benefitted greatly from his arrival.”
The board will now meet to discuss how to take the process forward.
The news will come as a blow to the FAI after an independent audit of its finances was last week referred to the Gardaí.
The audit was commissioned amid concerns over the association’s finances after it emerged former CEO John Delaney had given the association a €100,000 bridging loan from his own pocket.
That led Sport Ireland to 'suspend and withhold' State funding to the organisation, warning that it would not reinstate it until all reports and audits were complete.
It is believed Mr Foley had the backing of Sport Ireland.