Labour TD Ivana Bacik has said she is going to consult with party members over the weekend about whether she should seek to be elected party leader.
On Wednesday, Alan Kelly announced that he was stepping down from the role after the parliamentary party lost confidence in him.
He said he regretted that the party had not been able to make progress in the polls and did not get a bounce over the past two years.
This morning the party's executive board and parliamentary party met to agree the rules for the election of the new leader.
The meeting also agreed that Alan Kelly would continue in office as acting leader until a successor is elected.
There are strong indications that only Ivana Bacik will put her name forward for the position.
However, there were calls at today's meeting from party members to have a contest.
The party has decided that nominations for the post will close on Thursday 24 March and if there is just a single candidate they would take over as leader on that day.
If more than one candidate is nominated, an election will be held.
If there is a contested election, the date for the close of polling will be Friday 22 April.
A candidate may be nominated by either at least two Oireachtas members of the Parliamentary Party, or at last five constituency councils.
