The Director of Human Resources at the HSE Seán McGrath has said there has been a "steady trickle" of interest in the new redundancy and early retirement programme, since it was announced yesterday.
The HSE is to put a special calculator on its website today, to help health sector workers decide whether they will take voluntary redundancy.
It is hoped it will cut 5,000 jobs and save €200m a year, but staff need to register their interest in the next two weeks.
IMPACT, the union representing healthcare workers, is sceptical about the plan. Spokeperson Louise O' Donnell said the scheme will be attractive to some workers, but she believes the target will not be met.
"I am not convinced they will get the people they want," Ms O'Donnell said.
"I think what they will get is people on low incomes who, looking at the Budget coming down the road might decide that it would be better to get out of the workforce at this stage."
The HSE's HR Director Seán McGrath said it will work, but only if employees are flexible.
Mr McGrath said: "Ultimately, if people don't apply for this then we may have to redeploy them. We need flexibility within the system."