Two Progressive Democrat TDs and three senators have now publicly-backed Michael McDowell as the next leader of the party.
Junior Minister Tim O'Malley and backbench Deputy Noel Grealish, along with Senators Tom Morrissey, Kate Walsh and Michael Brennan, have said they would like to see Mr McDowell succeed Mary Harney.
Tim O'Malley said Mr McDowell was an unbelievably courageous politician and one who has had a profound influence for the good on Irish political life.
Noel Grealish said Mr McDowell was the right person to lead the party into the next General Election and would ensure that it continued to make a valuable and meaningful contribution to Irish society.
Although Mr McDowell has yet to declare his candidacy, it is thought certain he will put his name forward.
Neither of the other two possible candidates, Junior Minister Tom Parlon and PD whip Liz O'Donnell, have said if they will challenge him.
A further complication is that any candidate must be seconded by one of the party's eight TDs, which could prove difficult for Mr Parlon and Ms O'Donnell.
Contest would not benefit PDs: Molloy
The former minister, Bobby Molloy, has also given his backing to Mr McDowell. Speaking on RTÉ's News At One, Mr Molloy said he felt it would be of more benefit to the party if there was no contest for the leadership.
Also on the programme, the founding leader of the Progressive Democrats, Des O'Malley, paid a warm tribute to outgoing leader Mary Harney but would not be drawn on who should replace her.
Earlier, Mr Parlon confirmed that he may run for the leadership.
Meanwhile, the Minister for Foreign Affairs said he saw no reason why the Government could not run its full term despite Mary Harney's decision.
Speaking on RTÉ Radio, Dermot Ahern said he supported the Taoiseach's request that whoever succeeds Ms Harney would not take the PDs out of Government before the next election for party advantage.
The minister said he was not considering the possibility that Fianna Fáil might need to look for the support of Independent TDs.
Potential candidates have until Monday to declare their interest.
The new leader will be decided by a system of three party electoral colleges that gives more weight to votes from the parliamentary party.