Senator Gerard Craughwell has said it will be "difficult" to identify 20 Oireachtas members to sign his nomination papers to run for President.
Mr Craughwell told The Irish Times 17 people from across the Dáil and Seanad had pledged to support him, but the final few names were proving tough to secure.
The Senator said he would be contacting local authorities over the coming days to seek their support for his bid to run for presidency.
As reported at the weekend, President Michael D Higgins has indicated to Government he wishes to serve a second term in office.
Speaking to The Irish Times, Mr Craughwell said: "A lot of people have said they will support me. A few people have said they would but would not support if it is me versus Michael D.
“I accept we are getting to the stage where we are going to have to put names out there, and I will be discussing that with those who support me over the coming days. I will also be contacting local authorities too.”
Candidates require the signature of 20 Oireachtas members or four local authorities to sign their nomination papers.
As the incumbent Mr Higgins can nominate himself for a second term, but he has the public support of several Cabinet Ministers, including Shane Ross, Charlie Flanagan, Richard Bruton, Eoghan Murphy and Simon Harris.
Taoiseach Leo Varadkar has said he will wait until Mr Higgins publicly declares but believes there would be strong support for a second term.
Fianna Fáil has not declared, but it is understood party leader Micheál Martin does not believe the party should have a candidate on this occasion.
Sinn Féin leader Mary Lou McDonald has said her party will field a candidate if there is a contest. However, Ms McDonald has insisted Sinn Féin is very supportive of Mr Higgins.
A spokesman for Mr Higgins said the President would announce his intentions in early July.
Support
Mr Craughwell argued the President was delaying the announcement to prevent his challengers from securing support.
The Houses of the Oireachtas will rise on July 13th at the latest, and the Senator believes Mr Higgins will not confirm his intentions until after that date.
“Prospective candidates will find it very difficult to contact politicians during that period. Nobody is suggesting the President has not done a good job, but he should be reappointed by public support, not by coronation,” Mr Craughwell added.
The Government has provisionally set a date of October 26th for the vote, which will coincide with two referendums.
Minister for Justice Charlie Flanagan has secured Cabinet approval to hold a vote on removing the offence of blasphemy from the Constitution and a separate one on deleting a constitutional clause on the place of the woman in a home.
