The Supreme Court will be asked to exercise its "exceptional jurisdiction" to award costs in favour of Marie Fleming, the terminally ill Wicklow woman who lost her "right to die" case.
Ms Fleming lost her appeal against a High Court decision refusing her the right to assisted suicide earlier this year.
She has already been awarded the costs of the High Court case despite losing because of the issues of exceptional public importance involved in the case.
Her lawyers told the Supreme Court they would be making an application to the Supreme Court to make an order for costs in her favour, meaning the State would pay her legal costs.
Chief Justice Mrs Justice Susan Denham said it was a very important application and she would like to receive written submissions on the exceptional grounds to be put forward by Ms Fleming's legal team.
The costs hearing will take place in the autumn.
Ms Fleming has multiple sclerosis and would need help to end her life.
She believes her partner should not have to face criminal prosecution for helping her to do what an able-bodied person is free to do.
Both the High Court and the Supreme Court rejected her claim that the criminal law ban on assisted suicide breached her Constitutional rights.