Minister for Transport, Tourism and Sport Shane Ross has met newly appointed FAI independent chairman Roy Barrett and independent directors Catherine Guy and Liz Joyce.
Mr Ross, who was joined by Minister of State Brendan Griffin, emerged from the meeting in upbeat form and said: "It was good to have the opportunity to meet with the new chairman and directors so soon after their appointment.
"We had an encouraging and, frankly, a warm discussion today.
"I am now confident that the new board is committed to delivering the necessary governance reforms and ensuring that a stronger association emerges for the good of Irish football and all who love it.
"The old guard have now been excised and a healthy regeneration of the FAI can commence. We can now consider how best the Government can assist the FAI in moving on."
Mr Barrett, the managing director of Goodbody Stockbrokers, told RTÉ News that he was now hopeful the crisis in Irish football could be solved.
Mr Ross had earlier spoke of welcoming a "new chapter" in the history of the beleaguered organisation.
A fourth independent director is also set to be appointed in the coming weeks.
Speaking on RTÉ's Morning Ireland, Minister Ross said they are taking on the challenge of an organisation with €62 million debt.
"I'm very pleased to welcome Roy Barrett, Catherine Guy and Liz Joyce and to thank them as well for taking on what is going to be an extremely formidable task," he said.
"It certainly does seem that at this stage we are going to enter into a new chapter in what has been a disastrous story.
"They are taking on an association with a debt of €60m, they’re taking on a formidable challenge but we think that their advent, which has been sought for a very long time and which has been resisted by the FAI for a very long time, will mean that those who are creditors and stakeholders will take great encouragement."
While the minister insisted that the Government is not going to reward an association for wrong-doing, he said it does stand ready to assist and consider any plans that are being put forward.
He said creditors and stakeholders will take great encouragement in the new leadership and look to them as "a beacon of hope".
Government grants of approximately €2.9m per year to the FAI have been suspended since April last year.
The minister again reiterated his belief that in its current form the FAI is not fit for Government funding and a lot of conditions need to be met.
"We want to restore money and encourage projects to get people on the playing field," he said, adding that the association has to comply with "root and branch reforms first".
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Mr Ross revealed before Christmas that the cash-strapped organisation had sought €18m from the Government as part of a plan to restructure their finances, which he turned down.
The minister once again insisted that the Government would not be writing any blank cheques, but seemed to leave the door open to conditional support.
Talks between the FAI, the Government, UEFA, who have already given significant loans to the association, and Bank of Ireland are expected next week.
"We have got a new dawn here, a new opportunity," he said. "We have got new people who are going to produce a plan.
"Depending on that plan, and the conditions in which they will be imposed and implemented, and who the other stakeholders are, we are prepared to look at anything. We are not going to provide funding unconditionally to anybody.
"We've got to see that the League of Ireland is looked after because that’s got to be made a really, really healthy organisation.
"We’ve got to see that on the ground, grassroots football, which is the most important part, has got to be looked after and promoted as well, but we’ve got to do it in a healthy financial way."