Minister for Justice Michael McDowell is emerging as the favourite to replace Mary Harney as leader of the Progressive Democrats.
Five members of the PD parliamentary party have already said they will be backing Mr McDowell as the new party leader.
The Minister for Justice is widely expected to put himself forward for the position following Ms Harney's shock announcement yesterday that she would step down as soon as a new leader is found.
Other names linked with the job include Liz O'Donnell and Tom Parlon.
Junior Minister Tim O'Malley, Deputy Noel Grealish and Senators Michael Brennan, Tom Morrissey and Kate Walsh all said today that they would be backing Mr McDowell.
All of the PDs who were contactable this morning said they would prefer the party to agree on a candidate rather than hold a leadership contest.
Mr McDowell himself is remaining tight-lipped this morning about whether he will be throwing his hat in the ring.
Staff at his constituency office also say they know nothing of his intentions.
Monday is the closing date for nominations to the leadership position.
If more than one candidate applies, an election must be held within two months, with the new leader decided by a system of three electoral colleges.
The first group is made up the party's TDs and Senators and has 40% of the total vote.
The rank-and-file membership has 30% of the vote, while the remaining 30% goes to the national executive and the party's councillors across the country.