Loyalist paramilitary Michael Stone, who killed three people in west Belfast in 1988, is attempting to challenge a ruling that he must remain in prison until 2024.
He has instructed his lawyers to seek permission to appeal the verdict that six years he spent out on licence should not count towards his minimum term of imprisonment.
Earlier this week, judges at the High Court in Belfast held the Department of Justice had wrongly determined Stone is now eligible for possible release on parole.
Their finding came in a legal challenge mounted by the sister of one of his victims.
Deborah McGuinness's brother, Thomas McErlean, was among three mourners murdered in a grenade attack on an IRA funeral at Milltown Cemetery in March 1988.
The 63-year-old was also the gunman in another three separate killings.
Milkman Patrick Brady was murdered in south Belfast in November 1984, 12 months before joiner Kevin McPolin was shot in the head in Lisburn, Co Antrim.
In May 1987 Dermott Hackett, a bread van driver, was found dead in his vehicle between Drumquin and Omagh. He had been shot up to 16 times with a submachine gun.
Stone was freed early under the terms of the Good Friday Agreement in 2000.
Six years later, however, he was returned to jail after attempting to enter parliament buildings at Stormont, armed with explosives, knives and an axe, in an attempt to murder Sinn Féin's Gerry Adams and Martin McGuinness.
He denied it had been a bid to kill the politicians, claiming it was an act of performance art.
In 2013 he was told he must serve the remainder of a 30-year sentence imposed for waging a sectarian murder campaign.
The ex-UDA man's case had been referred to parole commissioners on the basis that he has now served that minimum term.
However, Ms McGuinness claimed the department unlawfully included the six years he spent out on licence before the attack on Stormont.
Her legal team insisted he should not be considered eligible for release until 2024 - when a full 30 years will have been served in custody.
They argued it was required for a sentence imposed to punish and deter Stone from future offences.
Backing the challenge by Ms McGuinness, the High Court held that he had forfeited the benefits of his exceptional early release when he returned to terrorist crime.
Mr Justice McCloskey said the earliest date Stone might be released on parole licence will be around July 2024.
Returning to court today, the prisoner's lawyers confirmed he is seeking leave to mount an appeal to the UK Supreme Court in London.
He can only get the required permission if it is established that the challenge raises a point of law of general public importance.
Adjourning the application, Mr Justice McCloskey asked the Department of Justice to disclose how many other parole cases could be affected by the ruling.
