Defence counsel Brendan Grehan SC, for Mr Hutch, today told the non-jury court that his legal team was in a position to proceed with the application.
However, the matter was adjourned until Monday as one of the three judges was unavailable.
Mr Hutch (58), who is in custody, was present in court for today's brief hearing with a full mane of grey hair to his shoulders and a full beard.
The three-judge court has to first determine a preliminary issue as to whether the Special Criminal Court has jurisdiction under Section 4E of the Criminal Procedure Act of 1967 to hear the application.
Section 4E states that a court can dismiss the charges against an accused person where there is insufficient evidence.
Defence counsel Michael O'Higgins SC for Jonathan Dowdall and Michael Bowman SC for Patrick Dowdall, who are to stand trial alongside Mr Hutch, said their clients were on bail in relation to the Regency Hotel charges and that they were also in a position to proceed.
In April 2021, former Sinn Fein councillor Jonathan Dowdall (43), with an address at Navan Road, Cabra, Dublin 7 was charged at the non-jury court with the murder of Mr Byrne at the hotel. Patrick Dowdall (64), also of the Navan Road, is accused of participating in or contributing to activity intending to or being reckless as to whether his actions could facilitate the murder of David Byrne. The indictment alleges that he made a room available at the hotel for a criminal organisation or its members on February 4, 2016.
All of the accused are due to stand trial at the Special Criminal Court on October 3 next. If the trial goes ahead, it is expected to last 12 weeks.
Ms Justice Tara Burns, presiding at the non-jury court, said she could not proceed with the application today as one of the three judges was unavailable. The matter was adjourned until Monday at 10.30am.
Last month, Ms Justice Burns agreed to hear a preliminary application to determine if the Special Criminal Court has jurisdiction under the Act to hear the application.
Information heard during such an application cannot be published or broadcast, save for any information the presiding judge permits to be published at the request of the accused.
David Byrne (34), from Crumlin, was shot dead at the hotel on the Swords Road in Dublin in February 2016 after five men, three disguised as armed gardaí, stormed the building, which was hosting a boxing weigh-in at the time.
Mr Hutch was extradited from Spain after his final appeal against extradition to Ireland was rejected by a Spanish Appeals Court on September 14. He was being held in a Madrid prison.
Mr Hutch is charged with the murder of David Byrne, contrary to Common Law, at the Regency Hotel on the Swords Road, Whitehall, Dublin 9, on February 5, 2016.
Mr Hutch has been in custody since being arrested in a restaurant in Fuengirola on the Costa del Sol in Spain on August 12, 2021 by the Guardia Civil. A search for him began in April 2021 after Ireland issued a European Arrest Warrant in connection with the attack on the Regency Hotel.
Mr Hutch, of The Paddocks, Clontarf, Dublin 3, is the third man to be charged with the murder of David Byrne at the Regency Hotel.
Separately, the Supreme Court has agreed to hear appeals by Mr Hutch and Jonathan Dowdall against the DPP's decision to try them before the non-jury Special Criminal Court.