Independent TD Maureen O'Sullivan and Fine Gael TDs Andrew Doyle and Bernard Durkan are to run for the position of Ceann Comhairle.
Ms O’Sullivan is said to have the support of a number of Independents in the race to replace incumbent Seán Barrett of Fine Gael, who has said he is not interested in retaining the post.
“It would be very historic to have a first female Ceann Comhairle. It would have to be part of an overall reform agenda,” said Ms O’Sullivan, a TD in Dublin Central. She said she wanted to thank Green Party leader Eamon Ryan, who first approached her about the position.
Mr Doyle, a Wicklow TD, is said to have the support of two Fine Gael Ministers for the position and will seek support from his colleagues at a parliamentary party meeting on Wednesday.
Mr Durkan, a TD for Kildare North, told the Irish Times he will let his name go forward for the role and is seeking the necessary seven signatures.
“It is a well established fact now that the Dáil system needs radical reform and we need to make it as effective as possible.”
Fine Gael will not support any single candidate in the election, which will take place when the Dáil resumes on Thursday.
There has been concern in Fine Gael that the election has become a party political decision, with Fianna Fáil and Sinn Féin both proposing a candidate.
Fianna Fáil TD Seán Ó Fearghaíl was chosen as the party’s candidate at a parliamentary party meeting on Monday afternoon.
The Kildare South TD was selected by the members over Brendan Smith, Michael Moynihan and Pat "the Cope" Gallagher.
Fianna Fáil leader Micheál Martin said Mr Ó Fearghaíl was well-respected across the political divide.
Sinn Féin’s Caoimhghín Ó Caoláin is also in the running.
