Simon Harris has become the first person to secure a nomination for the Fine Gael leadership.
The Higher Education Minister is seen as the clear frontrunner to succeed outgoing Taoiseach Leo Varadkar after his shock resignation yesterday.
Justice Minister Helen McEntee ruled herself out of the running this morning while Enterprise Minister Simon Coveney, who previously lost the Fine Gael leadership race to Mr Varadkar, has already ruled himself out.
Several Fine Gael party members have come out publicly to support Minister Harris this morning.
They include MEP Frances Fitzgerald, Senators Barry Ward, Tim Lombard and Martin Conway and TDs Frank Feighan and Neale Richmond.
Public Expenditure Minister Paschal Donohoe has yet to reveal his intentions.
Speaking in Dundalk this morning, Minister Donohoe refused to say whether he was running or who he would back – insisting, "I think it's all just a little bit too early for all of that".
Another potential candidate is Social Protection Minister Heather Humphreys who has yet to make her intentions clear.
Candidates need the backing of at least six members of Fine Gael's Parliamentary Party with voting taking place in early April.
'The best person to lead'
Fine Gael Senator Barry Ward told Newstalk Breakfast why he is backing Minister Harris.
"Nobody has declared yet but I will be nominating Simon Harris this morning," he said.
"I think he is the best person to lead the party into the future.
"He's somebody I've known for a very long time - over 20 years - and with whom I've worked particularly closely in the last number of years as well.
"I'm hoping that he will accede to that nomination and that he will be our next leader".
'Incredibly hard worker'
Senator Ward said Minister Harris understands the important issues.
"He's somebody I trust, he's somebody I think has huge capacity, he's an incredibly hard worker.
"He's also somebody who understands the issues and he has a different background to many of us.
"In the last year, Simon spent six months as Minister for Justice... and I saw up close and personal just how effective he can be".
Senator Ward said he believes Minister Harris is ready as he was Health Minister during the early months of the COVID-19 pandemic.
Simon Harris is set to officially announce his candidacy to replace Mr Varadkar this morning.