St Vincent's Healthcare Group is to hold a further meeting today with the Health Service Executive to discuss how it proposes to move towards compliance with public pay policy.
It follows a four-hour meeting of the group's board last Friday and an earlier meeting with HSE Director General Tony O'Brien on privately funded extra pay for three senior staff.
As part of the proposals, Chief Executive Nicholas Jermyn may have his salary paid entirely from private funds in future.
A manager may also be appointed to St Vincent's Public Hospital with that post entirely funded by the HSE.
Representatives of the group will appear before the Public Accounts Committee on Thursday to discuss the issue.
A resolution is likely to take some time, as the matters are complex and involve legal contracts, pension rights and governance changes.
The hospital confirmed in December that Mr Jermyn receives a salary of €292,669 from public and private funds.
This includes €136,282 from the public sector and €136,591 from the private sector, with a privately funded car allowance of €19,796.