Social Democrats co-leader Catherine Murphy has confirmed that the party will not go into coalition with Fianna Fáil and Fine Gael.
Speaking to RTÉ News, Ms Murphy said Fianna Fáil and Fine Gael have governed for the last four years and it was time for change.
She said there are critical issues like housing, health and services for people with disabilities that will not change if there is more of the same in government.
Ms Murphy said the Social Democrats were looking to see what kind of an alternative platform can be put together.
She said there are very early discussions under way on what process might be used to do that.
The party, which won six seats in the general election, says it is looking at the policies of the Green Party, Sinn Féin and Independents to see if common ground can be found.
However, Ms Murphy admitted there is a numbers issue with such an option.
She said it was a process and there can be no certainty about what the final outcome will be.
Fianna Fáil and Fine Gael have said they will meet early next week for exploratory talks.
Fine Gael has also said it will meet the Green Party.
The Dáil adjourned on Thursday until 5 March to allow parties to continue discussions on forming a Government.