The initiative received unanimous support back in April
Proposals to extend maternity leave to cover pre-mature births are expected to be approved by the Cabinet.
The initiative was originally recommended by the Green Party back in April.
The party had called for support for premature babies in Budget 2018, after unanimous passing of a Dáil motion supporting the proposal.
It will see extended benefit paid by the State for the period between the birth of the baby and when the leave would have commenced.
Social Protection Minister Regina Doherty is to bring the initiative to Cabinet.
A premature birth is described as one at less than 37 weeks gestation.
Speaking back in September, the Green Party deputy leader Catherine Martin said: "Every year in Ireland approximately 4,500 babies are born prematurely.
"One in 16 women deliver a preterm baby. At the time of the baby’s arrival, parents’ concerns, worries and anxieties are quite naturally focused on the baby’s safe well-being and progress.
"Maternity leave and maternity benefit may be one of last things on a mother’s mind but it won’t take long until the mother faces the reality of being treated by the State in a markedly different and unfair way compared to mothers fortunate enough to give birth to full term babies."
Under the Maternity Protection Acts 1994 and 2004, a mother is entitled to 26 weeks maternity leave and 16 weeks unpaid leave.
"Maternity leave comes into effect on the date of the birth of the child. However, babies surviving from the earliest gestations, such as 23 weeks, can spend months in a neonatal unit in hospital under the constant, watchful and nervous eye of their parents.
"By the time a premature baby gets to go home, a mother’s maternity leave can almost be used up," Deputy Martin added.
The extension proposed will cost in the region of €5m per year.