Fianna Fáil TD Éamon Ó Cuív has said he is making no comment on his interest or otherwise in contesting the presidential election.
"I am not saying anything to anybody," Mr Ó Cuív told The Irish Times.
Galway county councillor Noel Thomas said it had been a “mistake” for Fianna Fáil leader Micheál Martin to announce the party was not running a candidate without consulting with the wider membership.
Mr Martin confirmed in June his party would support President Michael D Higgins for a second term.
But Mr Thomas said: “I think that particularly if Sinn Féin is nominating a candidate, Fianna Fáil should also have one, and I think it has to be someone who had a statesman-like persona about them.”
“Éamon Ó Cuív fits that bill, although some might think his age would be against him – and not everyone agrees with his views.”
Galway county council Cathaoirleach, Seán Ó Tuairisg, has said Mr Ó Cuív would be an “excellent candidate” and Galway city councillor Ollie Crowe urged colleagues to back him.
However, Clare TD Timmy Dooley said: “If Éamon Ó Cuív or anyone else gets on to the ballot, they will do so as an Independent candidate.”
Mr Ó Cuív (68) is a grandson of president Éamon de Valera.
