Fianna Fáil and Fine Gael have appointed representatives to negotiate with other parties and Independents over coalition options.
Fianna Fáil won 48 seats in the general election, while their former coalition partners claimed 38.
Neither party is open to the option of a coalition with Sinn Féin (39 seats), so the options appear to be a deal with the Labour Party, Social Democrats, or Labour TDs.
Combined, Fianna Fáil and Fine Gael (86) are two seats short of a majority, although they will likely target more than 90 seats for a coalition to last five years.
Sources have indicated that both parties prefer a deal with Independent TDs, rather than Labour or the Social Democrats.
Taoiseach Simon Harris has confirmed that Paschal Donohoe and Helen McEntee will lead negotiations for Fine Gael.
Meanwhile, Tánaiste Micheál Martin has said Fianna Fáil's negotiating team will be chaired by outgoing Minister for Finance Jack Chambers.
The other members of the Fianna Fail team will be Darragh O'Brien, Norma Foley, Mary Butler, James Lawless and James Browne.
In government formation negotiations, Fine Gael will be eager not to come across as the clear junior party. It is interesting to note that their statement "mutual respect" and "parity".
A Fianna Fáil statement reads: "As we move into a formal phase of negotiations on the formation of a Government, I am pleased to announce the appointment of a Negotiations Steering Group to represent Fianna Fáil in discussions with other parties and independents.
"This group will oversee and coordinate engagements, working to develop agreed policy actions to address the pressing challenges facing our country. In addition, the group will ensure input and alignment with the Parliamentary Party throughout this process.
"The Negotiations Steering Group will comprise Jack Chambers (Chair), Darragh O'Brien, Norma Foley, Mary Butler, James Lawless and James Browne.
Fianna Fáil will approach these discussions in a positive and constructive manner as we work to deliver a stable and effective Government that meets the needs of the people."
