Dr Hegarty offered his resignation two weeks ago as bishop, citing an unspecified “irreversible” illness as the reason.
The 71-year-old Donegal native is also expected to feature in an forthcoming church-authorised investigation into the cover-up of clerical child abuse in his previous diocese, Raphoe.
Earlier this year senior Catholic officials visited Ireland to investigate how church structures should be reformed following a series of such scandals. Merging dioceses and eliminating bishops’ posts is one option.