Eight Independent TDs have formed a Dáil group that will give them speaking time in the chamber as well as positions on Oireachtas Committees.
The Regional Group of Independents is also willing to discuss government formation with Fianna Fáil and Fine Gael.
Michael Lowry has been appointed as the group's point of contact for any discussions with the leaders of Fianna Fáil and Fine Gael.
It is understood there is a view within the group that junior ministerial positions for Independent TDs should be on the agenda in government formation talks.
The group includes Michael Lowry, Sean Canney, Kevin 'Boxer' Moran, Noel Grealish, Marian Harkin, Barry Heneghan, Gillian Toole and Verona Murphy.
Ó Feargháil could serve third term as Ceann Comhairle
Meanwhile, the outgoing Ceann Comhairle Seán Ó Feargháil is said to be considering seeking a third term as chair of the Dáil.
A number of politicians confirmed tonight that the Fianna Fáil Kildare South TD is interested in putting his name forward as a candidate when TDs elect the next Ceann Comhairle on 18 December.
Earlier this year, Mr Ó Fearghaíl said he would return to the backbenches in the 34th Dáil having served two terms as Ceann Comhairle, which saw him automatically returned as a TD in last Friday's General Election.
The move has surprised several of his party colleagues given that TDs such as Brendan Smith, John McGuinness and Michael Moynihan have been linked with the prestigious role.
The matter was not discussed when the Fianna Fáil parliamentary party met.
Nomination papers for the election of Ceann Comhairle will be issued in the coming days.
Candidates need the backing of seven TDs to secure a nomination.
