Under the changes, hospitals within the six new hospital groups will be run by interim group boards, and these groups will eventually develop into independent hospital trusts.
Last year, Archbishop Martin told Minister Reilly that the current charter of Holles Street, which provides for the Dublin Archbishop to chair the board, is an 'anachronistic structure' that needed to be changed.
A Department of Health spokesperson told irishhealth.com that it was aware of Archbishop Martin's position regarding his chairmanship of the National Maternity Hospital.
The spokesman said under the hospital groups plan, Holles Street would now be part of the Dublin-East group of hospitals, and "governance arrangements related to Holles Stret will be dealt with in the context of the governance arrangements of the group."
Holes Street, under the planned abortion law, would become one of the designated centres where terminations could be carried out in accordance with the legislation.
The hospital reorganisation plan may lead to a dilution role of the Catholic Church in the governance of some voluntary hospitals.
While the majority of hospitals around the country are now State-run HSE hospitals, a number of hospitals, some of them Catholic, still have voluntary status and have their own boards.
The new hospital plan states that where one or more hospitals within a group have a pre-existing board, the hospitals in the group must work, through delegation of powers and common membership, to reach a position where the interim group board is the effective decision-making body for all hospitals in the group.
Hospitals still run by Catholic religious orders include the Mater and St Vincent's in Dublin.
Recently, the Catholic Bishops of Ireland expressed concern that the new legislation appeared to impose a duty on Catholic hospitals to provide abortions.
However the draft legislation only appears to provide for maternity units to carry out terminations in cases where the mother's life is deemed to be at real and substantial risk.
But only one of the 19 maternity units, Holles Street, can be termed a 'Catholic' Hospital due to its board being chaired by the Archbishop.
However, the Catholic Church has had no active role in policy direction at Holles Street in recent times.
It is thought likely that the current governance of Holles Street will be changed to comply with the new hospital groupings.
The Catholic Archbishop of Dublin also chairs the board of Crumlin Children's Hospital.