There are reports today that Joan Burton wants to stay on as the Labour Party leader.
It is thought both Ms Burton and the acting Environment Minister Alan Kelly would seek the post.
Labour Party rules require a leadership contest after a general election defeat.
It is also suggested in a report in the Irish Times that Joan Burton and Alan Kelly may support each other's nominations, as neither is certain of the backing of other party members.
In order to qualify, leadership candidates must be a sitting TD. They nominate themselves, but they must be seconded by another Deputy.
Former Labour TD for Clare Michael McNamara said the leadership should go to "someone who wants it anyway. It does appear that Joan wants it and it appears that Alan Kelly wants it. But it also appears they don’t have the support of even one other TD to nominate them.
"Obviously there would be support for Brendan Howlin, but whether he wants it or not is not clear. He hasn't made any announcement on it."