Nominations for Fine Gael leader will close on Sunday at 1pm, with Minister for Further and Higher Education Simon Harris widely expected to be the only candidate.
It follows a meeting today of the Fine Gael Executive Council.
The returning officer and chair of the party's executive council, Willie Geraghty, will make an announcement at the conclusion of the party's Midlands Northwest selection convention in Athlone on Sunday afternoon to declare the winner.
Mr Harris - who has been backed by a large portion of the Fine Gael parliamentary party to succeed Leo Varadkar as leader - has said that while he is not ruling anything out, a general election is not his priority.
Speaking in Co Meath this morning, Mr Harris said that if he becomes leader he will "remain committed to the programme for government" and to working with Fianna Fáil and the Green Party.
He said that his priority was the election of a Fine Gael leader, and that a "general election is not in any manner or means on my mind".
"The people of this country want us to get on with their business," he said.
This morning, Minister for Public Expenditure Paschal Donohoe confirmed he too would support Mr Harris for the position of party leader and Taoiseach.
Speaking after he addressed the European Council in his capacity as Eurogroup president, he said he had not discussed his ministerial future with Mr Harris but would relish the opportunity to continue his work.
Asked if it was imperative that he continue as Public Expenditure to remain as Eurogroup president, he pointed out that the holder of that role almost always serves in a finance portfolio.
"There were a few months when that was not case but I think it is something that other ministers would love to be led by a minister (for finance/public expenditure) but that is not really the focus of my thoughts here today," he said.
Mr Harris has already received support from nearly half of the parliamentary party, including a series of ministers including Helen McEntee and Heather Humphreys.
He would not be drawn on who will be in his new cabinet, if he becomes Taoiseach, saying that as of today he is not the leader of Fine Gael.
He said if there is no contest, there will be "an important period of time" to make those decisions.
"If there is no contest, that will provide the new leader with a period of space between becoming leader of Fine Gael and then ultimately seeking to put together a government in Dáil Eireann, and ask Dáil Eireann for a mandate, and that would be an important period of time," he said.
Mr Harris said there are "very talented" people in the parliamentary party, and he looked forward to "having the opportunity to showcase those talents".
"That's a matter for another day," he added.
"I have great colleagues that I serve with every single day, Helen McEntee is a great colleague, and I'm looking forward to asking everybody to step up and serve in roles that are, in my view, best suited to their talents and ability to deliver, should I have the opportunity to serve," he said.
Minister Harris was attending breakfast meeting with Fine Gael members in support of local election candidate Sharon Tolan at the City North Hotel in Gormanston.
The breakfast was also attended by Meath TD and Minister for Justice Helen McEntee, along with MEP Colm Markey, and newly announced candidate for the European elections Nina Carberry.
Mr Harris said the last few days had been "quite a whirlwind", and thanked Mr Varadkar for "his leadership and how he has represented our country at home and abroad".
"I am overwhelmed and honoured by the level of support I have received over the las number of hours," he said.
Mr Harris said his commitment to his party and the people of the country, if he is successful in his bid to become leader, was that: "I will give this my all".
Varadkar dismisses conspiracy theories around resignation
Outgoing Taoiseach Leo Varadkar has said that he understood the need for conspiracy theories following his surprise resignation announcement earlier this week, but he is not aware of "some sort of scandal that is about to break".
"That's not to say that somebody isn't going to throw some allegation at me tomorrow, next week, or in a few month's time that I'm not aware of now, that will probably be a load of rubbish like most of them are.
"People will then turn around and say: 'Aha, that was the real reason'. But like, that's not... if you want to do that, fine," he said.
Speaking at a European Council meeting in Brussels, he also said Cabinet reshuffles were one of the hardest parts of his job and he is not sure they can ever be done exactly right.
He said on the day a person is elected Taoiseach, family and friends are delighted for them.
However all he could think about on those days were the "awful set of meetings" where he would have to tell many people that there were being demoted or moved sideways.
He defended his own Cabinet choices, though, saying "I was blessed by the people I had around me. They were so good."
Given that Mr Harris looks firmly on track to become the next Taoiseach, Mr Varadkar was asked if he had any plans to recall the Dáil early during the Easter break to accelerate this process.
He said there were no plans to do so unless the other Government party leaders request it.
Next Taoiseach needs to speak to parties - Collins
The next Taoiseach will need to talk to other parties to get their support, according to the leader of one of Ireland's newest political parties.
Michael Collins, who is leader of the Independent Ireland party, said on RTÉ's Morning Ireland that if Mr Harris wants to become Taoiseach "he needs to sit down and talk to a party like Independent Ireland and others that he seeks that support from".
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Independent Ireland currently has three TDs - Mr Collins, Limerick TD Richard O'Donoghue and Roscommon-Galway TD Michael Fitzmaurice.
"We need a major change of Government policy. The disruptive green policies that are there at the moment will have to stop because they're affecting people, especially in rural communities and especially farmers, agriculture and people that are doing business," Mr Collins said.
"But it's not just rural issues that the new Taoiseach, incoming Taoiseach, most likely Simon Harris, will have to deal with.
"He has to look at the tourism business, where we have 280 restaurants and cafes after closing over the last couple of months.
He said that restoring the VAT rate from 9% to 13% for the hospitality sector "absolutely decimated small businesses like cafes".
Mr Collins said that he and his party will never refuse to meet an incoming Taoiseach.
"Because we need to see a change of direction from this Government. As I said, agriculture and fisheries and issues like that have been completely neglected by the last government, and if they're not going to be dealt with this Government, we cannot support this Taoiseach coming in."
Mr Collins also said that there needs to be a change to immigration policy "because we can't have people coming to this country that are living in tents".
Labour TD Duncan Smith has said it was clear to those who had been on the frontline of politics that Leo Varadkar had "become an electoral liability to Fine Gael".
Speaking on RTÉ's Today with Claire Byrne, Deputy Smith suggested that Mr Varadkar was "tapped on the shoulder" and told he had to go.
He said he does not think having a "temporary Taoiseach" in Simon Harris would work for Fine Gael and that it would be "more appropriate" to have a general election.
Speaking on the same programme, Fianna Fáil Senator Lisa Chambers said Mr Varadkar's resignation presents a "distraction" for some Cabinet ministers while Fine Gael undergoes a leadership change.
She said she took his reasons for stepping down at face value and criticised those who did "just wish him well".
"There was just a level of bitterness and coarseness and a lack of decency on that day," she said, adding that there was a limit to what any person could take while doing that job.
Coveney not lobbying for Cabinet position
Minister for Enterprise, Trade and Employment Simon Coveney has said he remains committed to running in the next general election and contributing to the work of Government, but said he is not going to speculate about his future in the Cabinet.
Speaking this morning in Co Cork, Minister Coveney said he would not be lobbying publicly for a position in Simon Harris' Cabinet.
He said he had a good relationship with Simon Harris and he wished him well as he bids to become the next leader of Fine Gael and Taoiseach.
Asked if he was confident he would be in Minister Harris' Cabinet, Mr Coveney said: "I'm not going to start speculating about that.
"We have been through a week where extraordinary change has happened very, very quickly. We are now on our way to confirming a new leader in Fine Gael and someone who is going to put themselves before the Dáil as the likely next Taoiseach and I wish Simon Harris well in that."
The minister said Simon Harris had moved quickly to secure "very strong endorsements" across the party.
Asked why he did not endorse Mr Harris' leadership bid when he announced that he would not be a candidate himself, Minister Coveney said: "First of all, the actual formal process of finalising selection of a new leader isn't over so, I think correctly, [I] wanted to give that process some time and I did.
"I have been in contact with Simon Harris, but I didn't feel the need to be first out or anything like that. My relationship with Simon Harris is a good one. He knows my feelings on these things.
"I have also got a good relationship with others in the party, some of whom were considering running for leadership for a period of time and I respected that and I wanted to give people the time and space to consider that. It is nothing more or less than that."
Mr Coveney said he also remained committed to running in next general election: "I am, and I hope to contribute positively to the work of the Government. We have a lot of work to do in the months ahead and I remain committed to politics, as I have been."
He said he felt Fine Gael would probably be strengthened by having a new leader heading into the local and European elections in June.
Additional reporting: Laura Hogan, Micheál Lehane, Paschal Sheehy
