The Government says it will "continue the process of dismantling the HSE, evolving it into a health commission"
A Fianna Fáil TD says if the Government tries to scrap the HSE they will vote against it.
New Health Minister Simon Harris is understood to have plans to dismantle the HSE.
They plan to replace it with a health commission and trusts to manage hospitals.
In the Programme for Government, the section on health states that "we will advance progress made on Hospital Groups before strengthening their capacity to be stand-alone statutory Trusts.
"Hospital Trusts will gain greater autonomy (own their own assets, manage recruitment) while also ensuring accountability," it adds.
However, Fianna Fáil and other Opposition parties are against the move.
TD Thomas Byrne says that, despite their support agreement with Fine Gael, they would vote against the scrapping of the executive if it came before the Dáil.
Speaking to Newstalk Breakfast, he said "there's a better way to do things in terms of collaboration - clearly on this issue there is a fundamental disagreement between the Government party, the Independents who prop them up and Fianna Fáil".
He suggests a better solution would be to "sit around a health committee and the Dáil chamber itself to work out how best we deal with the hospital crisis".