The FAI has stepped up security at its Abbotstown headquarters in Dublin, with An Garda Síochána confirming they are investigating threatening letters sent to the association.
It has not been confirmed if the material posted was in response to financial troubles at the association disclosed last week.
In an email to staff, interim chief executive Paul Cooke said extra security measures have been put in place as a "precautionary mechanism".
On Tuesday, the FAI board has said they would be "unable" to attend an emergency Oireachtas Committee meeting that had been scheduled to take place today.
The Joint Oireachtas Committee on Transport, Tourism and Sport had invited the FAI to the meeting to discuss the dire financial situation at the association, but the FAI released a statement saying that their board would not be in attendance because they are currently focused on a refinancing package that will "guarantee the future of the FAI and safeguard jobs".
Last Friday, the FAI disclosed that the organisation has current net liabilities of more than €55m, with auditors Deloitte unable to guarantee that the governing body can continue as a going concern.