The Progressive Democrat Senator, Tom Morrissey, has said that he would be contesting the leadership of the party.
Mr Morrissey said that what was needed was a 'general election' of all the members of the PDs.
Former TD Fiona O'Malley also indicated that she would be interested in leading the party.
They were speaking as a meeting of the party's General Council got under way this lunchtime at a hotel at Liffey Valley in Dublin.
Party members are being told of proposals to deal with the election of their next leader.
It was announced at the meeting that the Minister for Health, Mary Harney, will stay on as caretaker until the autumn.
The PD National Executive has already appointed a five-person committee which will produce a report in the autumn on changing the way leadership candidates are nominated and how the election is carried out.
The party said that this meeting was about taking soundings from the membership.
Under existing rules, the parliamentary party has 40% of the votes in the leadership election, with 30% going to councillors and another 30% going to ordinary members.
