Minister for Justice Charlie Flanagan has said some of the names mentioned in the race to contest President Michael D Higgins "should not be taken seriously".
Mr Higgins has not confirmed if he intends to seek a second term in office but it is believed he has informed political leaders he may require their support.
A number of Independent TDs and senators and others including artist Kevin Sharkey have confirmed they wish to contest for the position.
Speaking to The Irish Times, Mr Flanagan said he was fully supportive of Mr Higgins remaining in office unopposed.
“The head of State is a serious position. With the greatest of respect to some names being speculated upon, they cannot be taken seriously. They wouldn’t hold a candle to the current President,” he said.
Independent senators Gerard Craughwell and Pádraig Ó Céidigh, Fianna Fáil senators Mark Daly and Keith Swanick and Independent TD Michael Fitzmaurice have been linked with the role and have not ruled out contesting a presidential election.
An election for the office of president is due to take place later this year and Mr Higgins is expected to make his intentions known by July.
Support for Higgins
Fine Gael and Fianna Fáil have declined to be drawn on whether they will field a candidate in an election. Both party leaders have stated their support for Mr Higgins.
Speaking on Wednesday, Fianna Fáil's spokesman on social protection Willie O'Dea confirmed he could not support former taoiseach Bertie Ahern if he chose to run as an Independent candidate.
Mr Ahern told The Irish Independent he was willing to run but would not stand against Mr Higgins, insisting the current President would win.
He would not seek Fianna Fáil’s support, however, and would position himself as Independent.
Mr O’Dea said he is a member of Fianna Fáil and could not back an Independent.
He added: “My own personal view is that Michael D has done a good job. I can’t anticipate whether or no there is going to be a contest but he has done a good job and he has represented the country very well.
“I won’t lose any sleep if Michael D decides to stand again and is returned or is returned unopposed, it won’t trouble me in any way.”
Sinn Féin leader Mary Lou McDonald has said the party would field a candidate if there was a contest, and has said she believes there should be.
It is understood TD for Cavan-Monaghan Caoimhghín Ó Caoláin is one of the names being considered by the party.
Elsewhere, Minister of State John Halligan told The Irish Times the Independent Alliance was not opposed to a contest taking place but stressed he and others would be supporting Mr Higgins.
Mr Halligan said it was extremely unlikely the group would support the nomination of Senator Gerard Craughwell.
Mr Craughwell had been a member of the group up until 2016 but left after a dispute with the members over his role in the negotiations on Government formation.
Independent Alliance TD Seán Canney said there had been no discussion in the group on what it should do.
He believes there should be a contest but added Mr Higgins would win an election regardless.
