Labour Party deputy leader Alan Kelly has insisted party members should have their say in the election of a new leader.
Mr Kelly declined to answer questions about whether he had a seconder to back his nomination for leader.
Mr Kelly said that was a question for his colleagues in the parliamentary party rather than him.
However, Mr Kelly said Labour supporters were entitled to a vote on the leadership.
Former minister for public expenditure and reform Brendan Howlin said an internal discussion was underway in the parliamentary party about the leadership.
Mr Howlin said this was bigger than who the next leader will be and the party needed to rebuild and reconnect with the electorate.
Cork TD Sean Sherlock confirmed he had not made up his mind on whether to contest for the position.
The party on Thursday published a Bill proposing that the Constitution be amended to ensure provide for certain public utilities to remain in public ownership.
Leader Joan Burton said the new Government would not provide the same protection to public utilities as the outgoing one had.
She said: “As far as Labour is concerned the provision of water could never, and should never be something that can be outsourced to the private sector.
“However, there is now a new political reality and I believe that if push come to shove, the current Government would take a very different view on the ownership of indeed potential sale of key state assets and state commercial companies.”
Former minister for public expenditure and reform Brendan Howlin said the party will never be recognised for what it prevented in government.
He said Labour stopped the further privatisation of State assets.