Mr. Reilly, whose daughter Amber died in February 2010, one week after she was delivered in the Galway hospital, hopes to have his family's case included in the inquiry which predominantly focuses on incidents from 2014.
The inquiry is due to cover circumstances in which oxygen-deprived infants were delivered at the hospital last year, two of whom did not survive.
A statement released by the hospital and healthcare group says: "Families affected will be consulted fully and the findings of any reviews will be made available to the families."
The Reilly family have been told that their issues will be taken "fully into account" when considering the terms of reference.
A further four families are due to be met with next week to discuss the matter.
Services in the hospital have been called into question in recent months with families demanding answers regarding the treatment they received while under Portiuncula's care.
