Galway West TD Noel Grealish and Galway East TD Sean Canney will engage in Government formation talks in the coming days.
The two Galway TDs are part of the Regional Independent group of TD's, who could be set to become the third leg of the new Government.
Kerry Independent Deputies Michael and Danny Healy-Rae will also be invited to take part in formal discussions.
Meanwhile, its expected the Social Democrats will announce its intention to end contact with the bigger parties, and remain in opposition.
