There are set to be at least four candidates put forward for the role Ceann Comhairle when the Dáil meets next week.
Independent candidates are set to put forward an agreed candidate, with Maureen O'Sullivan of Dublin Central saying she is 'thinking about' putting her name forward.
Earlier today independents John Halligan and Finian McGrath - both of whom had been tipped for the role - ruled themselves out, saying they would prefer to focus on constituency work.
Sinn Féin is putting forward its longest-serving TD, Caoimhghín Ó Caoláin, who has been a member of the Dáil since 1997.
Fianna Fáil will meet on Monday to choose an agreed candidate from among four contenders. Pat 'the Cope' Gallagher, Michael Moynihan, Seán Ó Fearghaíl and Brendan Smith have all been touted as contenders.
The outgoing coalition is expected to put forward at least one candidate too, with Fine Gael's John Deasy and Fergus O'Dowd mentioned.
The name of Labour's Brendan Howlin - who previously served as Leas Ceann Comhairle - has also been mentioned, but his is considered an unlikely candidate, given Labour's depleted strength on the back benches and its need for strong performers.
However the Dáil rules would allow Labour to retain its speaking rights even if Howlin were to take the role, as the rules only require a party to have been elected with seven TDs, and not necessarily to retain that number.
The role of Ceann Comhairle may be particularly prized in the forthcoming Dáil as the possibility of a second election remains realistic. The holder of the office is automatically returned at the next election - meaning, for example, if Maureen O'Sullivan were to take the role, only two of Dublin Central's three seats would be available next time.