HSE bosses are looking for almost €2bn more in budget funding for 2016.
The request made in a written submission comes as estimates from the Executive now put the overrun for this year alone at around half a billion euro.
The extra funding outlined by HSE management would be channelled into three main areas.
They are meeting the overrun on this year's expenditure, providing the same level of services at facilities around the country in 2016 and also bringing a range of hospitals and elderly services up to standard.
Details are contained in a confidential submission, seen by the Irish Independent, which was sent to the Department of Health three weeks ago.
The €2bn demand would absorb all of the financial leeway that the Government is expecting to have as it prepares Budget 2016.
However, the Director General of the HSE Tony O'Brien warns in the submission that if they "simply stand still", they won't be in a position to address the needs of the population as it grows and ages in the years ahead.