Galway West TD Hildegarde Naughton is in the frame for promotion to full ministry, as cabinet ministers are set to be appointed today.
Micheál Martin will be formally elected as Taoiseach later as a new Government forms, almost two months on from the general election.
Reports today suggest Fine Gael Deputy Naughton is among four names being considered for two promotion positions.
Once Micheal Martin receives his seal of office from President Michael D Higgins, Micheál Martin will start appointing his Cabinet.
Martin has seven roles to offer his own party - Jack Chambers, Darragh O'Brien and Norma Foley are seen as locks.
With Charlie McConalogue, Mary Butler, James Browne, Dara Calleary, Thomas Byrne and Jim O'Callaghan all likely to be considered for the other roles
On the Fine Gael side Simon Harris, Helen McEntee and Paschal Donohoe will all return to Cabinet - with Patrick O'Donovan and Peter Burke also heavily favoured.
That leaves him two spaces for promotion to a full ministry - Jennifer Carroll MacNeill, Martin Heydon, Hildegarde Naughton and possibly Alan Dillon are in the frame there.
