It's the first set of meetings due to take place since the party agreed a deal with Fianna Fáil on Friday.
First up the Independent Alliance will meet with negotiators this morning – with the issue of a cardiac care centre for the South East believed to be the major stumbling block.
Fine Gael needs the support of six more TDs in order to elect Enda Kenny Taoiseach on Wednesday.
Tipperary TD Mattie McGrath of the so called Rural Alliance says there's still more work to be done – particularly on paying for upgrades to the water infrastructure.
