A meeting is expected to take place this week between the Taoiseach, Tánaiste and Health Minister to consider options for the location for the new National Children's Hospital.
James Reilly will present an analysis of the issue and the main options.
If agreement is reached, a memo will be prepared for Cabinet and for a Government decision on the location.
It is understood that around four locations are being considered.
They include the Mater hospital, St James's Hospital, Connolly Hospital Blanchardstown, and a site in northeast Dublin called Belcamp.
The Dolphin Review group received 41 site submissions and presented its report to the minister on 8 June.
Speaking in Castlebar, Enda Kenny said Mr Reilly was reflecting on the Dolphin Report and recommendations would be forthcoming in the next ten days.
He said a collective Cabinet decision would then be taken.
Responding to the ongoing controversy surrounding additional locations for primary care sites, Mr Kenny also said he continues to have full confidence in Mr Reilly.
He said Fine Gael and Labour had a clear Programme for Government to implement and would not be diverted by an agenda of vested interests.
Asked about the level of consultation he had with Mr Reilly about the additional sites, Mr Kenny said the matter had been dealt with ad nauseam and the Government is moving on.