Cavan and Monaghan could have two Government Ministers if agreement is reached between Fine Gael, Fianna Fáil and the Green Party.
Speculation is mounting on who will fill what posts as an agreement is expected before the end of next week.
The parties will continue to meet with other TDs today when they meet the eight deputies from the Regional Group this afternoon.
It's believed Fianna Fáil TD Brendan Smith will be nominated to the role of Leas Ceann Comhairle.
Michael Brennan from the Business Post told The Joe Finnegan Show today that Fine Gael's Heather Humphreys is expected to retain a Cabinet seat.
And he said Fianna Fáil's Niamh Smyth could also be looking at a ministerial portfolio: