The party is attempting to win the presidency for the first time.
Party chiefs held discussions last week where it was agreed to host a meeting of FG’s electoral college in a number of weeks to vote on who will go forward as its presidential candidate.
The emergence of the proposed party vote will pile pressure on the remaining parties to publicly declare which candidates they are considering.
With at least half a dozen individuals from different political spectrums already in the running, Fianna Fáil and Sinn Féin have yet to reveal who will lead their race for Áras an Uachtarán.
FG MEP Mairead McGuinness this month announced her bid to run, while fellow party MEP Sean Kelly is also believed to be considering running.
Former taoiseach and FG vice-president John Bruton was thought likely as a possible candidate but that is now in doubt after a recent interview in which he said he had “no ambitions in that direction”.
Former president of the European Parliament Pat Cox is also thought to be interested in a nomination from Fine Gael and has not ruled out running.
At a party executive council meeting last week, it was decided to hold the party’s selection convention in June. All candidates will meet with the electoral college there, whose vote is made up of the parliamentary party (70%), councillors (20%) and the national executive (10%).
Labour has not decided when it will hold its selection convention but former TD Michael D Higgins and Barnardo’s chief executive Fergus Finlay are both competing for selection.
Fianna Fáil are remaining tightlipped about their options, although party sources say Brian Crowley, Ireland’s longest-serving MEP, is likely to be the only candidate backed by the party and that former Taoiseach Bertie Ahern and Senator Mary White, despite reports, are unlikely to run.
Independent Senator David Norris is the bookies’ early favourite, although he will need the backing of at least 20 TDs or the support of county councillors.
The Constitution states that every candidate for the presidential election must be nominated by either 20 members of the Oireachtas or by four local authorities.
Reports that some parties have told their councillors not to support Mr Norris’s nomination were not commented on by his backers.
A date in early November is being mooted as the day when voters will decide on the election of Ireland’s ninth president, to replace President Mary McAleese.