The Labour Party's national executive committee is due to meet tomorrow to decide on a closing date for nominations for the posts of leader and deputy leader.
An estimated 4,000 party members, who have been fully paid up for the last two years, will be entitled to vote.
Dún Laoghaire TD Eamon Gilmore, who is firm favourite to become the next leader, remains the only deputy to declare his candidacy for the post.
Mr Gilmore has received the backing of former leader Ruairí Quinn and the current chief whip Emmet Stagg.
His chances were significantly boosted yesterday when finance spokeswoman Joan Burton surprised colleagues by announcing she would not be contesting the leadership of the party, but will seek the deputy leadership instead.
The current acting leader of the party, Liz McManus, yesterday reiterated she would not announce her leadership intentions until after the national executive meeting.
That meeting is expected to set next Thursday as the deadline for close of nominations.
Dublin North East's Tommy Broughan, the only other TD still considering entering the race, was expected to announce his decision today.
So far Ms Burton and Limerick East TD Jan O'Sullivan are the only candidates to declare themselves interested in the deputy leadership post. Cork South Central TD Ciarán Lynch said he was also considering running for this position.
Earlier in the week, Wexford TD Brendan Howlin and Dublin North West TD Róisín Shortall both ruled themselves out of the leadership race.
Pat Rabbitte resigned as leader last week following a disappointing general election in which the party failed to make the hoped-for breakthrough.