The Government will seek "an early meeting" with UEFA following Monday's talks with FAI officials at Leinster House.
Minister for Tourism, Transport and Sport Shane Ross and the Department's Minister for State Brendan Griffin met with five directors and FAI vice-president Paul Cooke, along with financial advisers from Grant Thornton to discuss the current situation within Irish football's governing body.
In a statement, Ross and Griffin outlined that the organisation "accepted" a number of points raised during the meeting. That includes the need for the appointments of an independent CEO, chair and directors as well as a "culture change".
Last Thursday, the FAI had confirmed that they have "identified their preferred candidate for the role of the independent chairperson of the organisation" from a three-person shortlist.
In Monday night's statement, Ministers Ross and Griffin stated that they want a meeting in the "coming days" with European football's governing body UEFA.
Tonight Ministers Ross and Griffin, with their officials, met with 5 directors and Vice President Paul Cooke, with their financial advisers from Grant Thornton, in Leinster House.
The FAI directors accepted the need for all previous directors to exit.
The FAI directors accepted the need for a full change of culture in the organisation.
The FAI directors accepted the need for the independent Chair and directors to be appointed urgently.
The FAI directors accepted the need for the appointment of an independent CEO without undue delay.
The Ministers reiterated that the FAI is in a dark place, the brand has been damaged and much work needs to be done.
Minister Ross & Griffin have said: "The KOSI report stated that an unreformed FAI was unfit to receive government funding. That process of reform is still far from complete.
"The government cannot provide direct financial support to the FAI. We are finalising a mechanism to get our youth field programme funding to the front line. Our priorities are players at every level, staff in the organisation, volunteers across the country and supporters.
"We will be seeking an early meeting with UEFA in the coming days to intensify the search for a solution to the deep problems inflicted on the FAI."
Speaking to Off The Ball last Friday, Senator Aodhan O'Riordain commented that in his view, UEFA "don't want to have a controversy around Irish football when they arrive here next summer for the European Championships 2020".
Meanwhile, the FAI board also released a statement on Monday night, thanking Ministers Ross and Griffin for meeting with them.
Cooke described the talks as "constructive".
The Board of the Football Association of Ireland has thanked Sports Ministers Shane Ross and Brendan Griffin for an open and honest meeting at Leinster House this evening.
A six-strong delegation from the Board, led by interim Executive Lead Paul Cooke, met with the two Ministers and leading Department of Sport officials for over 90 minutes.
"The talks were constructive,” said Cooke afterwards, "We outlined our position as regards the current financial situation at the FAI, our ongoing governance reforms and culture change and where we go from here.
"We stressed how the immediate focus of the Board and the Association has to be on the financial restructuring necessary to safeguard jobs, the FAI’s financial future and the appointment of an Independent Chairperson and three Independent Directors.
"We look forward to engaging further with the Ministers and the Department of Sport as we agree on the next steps."