The Minister for Agriculture and Defence Simon Coveney says there is a sense of urgency in forming the next Government.
It comes as Fine Gael is due to meet with the six members of the Independent Alliance this morning.
Enda Kenny needs the support of six more TD's to become Taoiseach
Yesterday Independent Alliance TD John Halligan said he wouldn't be supporting a Fine Gael Minority Government - if they didn't meet his demands for 24-hour cardiac care at Waterford hospital.
But at this stage Minister Coveney is optimistic that a deal could be done by Thursday:
However the Independent Alliance doesn't believe a Government will be formed this week.
Shane Ross says they've yet to see the draft deal worked out between Fine Gael and Fianna Fáil: