The Department of Health has said an "improved" salary is to be paid to the new head of the HSE in order to attract a suitably qualified candidate for the job.
The post has been vacant for the past six months, and has been advertised twice.
Three potential candidates interviewed for the position earlier this year, but none were successful.
In a statement to RTÉ's This Week programme, a spokeswoman for the Minister said "a recruitment package commensurate with the importance of the role will be provided to the successful candidate".
"Full details will be agreed as part of the final contract negotiations. As part of the competition under way, the Minister envisages that improved terms will be available should this be necessary to secure the most suitable candidate."
It is understood the salary on offer for the position was around €250,000, but this may now be increased.
The Chairperson of the Oireachtas Health Committee, Dr Michael Harty, said he was concerned that it is taking so long to fill the position.
"Not having a Director General of the health service is an impediment to the proper governance of the HSE.
"The HSE has a budget of €17bn and it's very important that you have a person in place to drive the management of the system forward," said Dr Harty.
He said the Government should go into the international market and provide a higher salary to attract a suitable candidate.
"The salary on offer at the moment is similar to that which is available to middle management positions in the NHS (the UK's National Health Service) so you're not going to attract someone of the calibre needed on that salary, so it should be increased," he said.
Asked if there should be upper limit on the salary available to the new HSE boss, Dr Harty said "it's very difficult to say what that upper limit would be".
Dr Harty also suggested that political interference in the running of the HSE had turned candidates off applying for the job.
He said there should be a constructive integration between the Department of Health and the HSE.
A spokeswoman for Minister Simon Harris said the new CEO of the health service would be accountable to a newly appointed board, rather than directly to the Minister.
"It is important to state the new CEO will operate under the direction of an independent board, as provided for in the Health Service Executive (Governance) Bill which is currently before the Oireachtas."
"Mr Ciaran Devane has been appointed Chair and the Minister expects to be in a position to appoint other board members soon. The passing of this legislation and finalisation of the membership of the board, based upon competency, will allow it to come into operation in the new year," she said.