The Sinn Fein leader has suggested his party could support a minority government led by either Fine Gael or Fianna Fáil.
But Gerry Adams says he would have to 'wait and see' what proposals were put on the table by either party.
His party is maintaining its position that it will not act as a junior partner in a government led by Fine Gael or Fianna Fáil, in line with the party policy agreed at its last Ard Fheis.
But Sinn Féin has also conceded that it does not have enough of a mandate to form a left-wing government, and that therefore any coalition will inevitably be led by either of the two larger parties.
Talks are continuing today between various parties in an effort to build a government before the Dáil meets for the first time on Thursday.
Our political correspondent Gavan Reilly reports:
Meanwhile the Independent Alliance says it's expecting a reply from Enda Kenny early next week about its demands for government.
Four of the alliance's six TDs met with Kenny this morning, at his request, to discuss their ten-point 'Charter for Change'.
It says the Fine Gael leader will reply in detail to their demands early next week.
Waterford TD John Halligan says the Taoiseach himself also put some offers on the table: