Lawyers for Sean McGovern, who is charged with murder and directing a criminal organisation, have raised a concern about the legality of his extradition to Ireland from the United Arab Emirates last week.
The 39-year-old's barrister Olan Callanan told the Special Criminal Court that Michael Staines' solicitors office will issue a letter to the Director of Public Prosecutions imminently, putting the DPP on notice of an application.
Mr Callanan asked the three-judge, non-jury court to set a date for a hearing, adding: "The fundamental concern is the legality, the propriety and the process which surrounded his arrival in Dublin".
On 29 May, when Mr McGovern arrived in Dublin and was first brought before the court, Mr Callanan said he was reserving his position on the legality of the process and the jurisdiction of the court.
Senior Counsel Sean Gillane, for the DPP, told the court that a first book of evidence relating to the charges against McGovern will be ready by the end of next month.
The DPP will update the court on a second book of evidence at a later date.
Mr McGovern viewed today's proceedings via video-link from prison. He spoke only to confirm that he could hear what was being said.
Ms Justice Karen O'Connor agreed to hear McGovern's application on Wednesday, 18 June. He will again appear by video-link rather than in person.
The court set a date in late July for service of the book of evidence.
An Irish Air Corps Casa 295 plane took Mr McGovern from Dubai to Dublin last week, stopping off in Larnaca in Cyprus and Marseille in France to refuel.
It landed at Casement Aerodrome in west Dublin, before gardaí brought Mr McGovern before the Special Criminal Court on five charges.
Mr McGovern, with a previous address at Kildare Road, Crumlin in Dublin, is charged with the murder of Noel Kirwan on 22 December 2016 at St Ronan's Drive, Clondalkin in Dublin.
He is accused of directing the activities of a criminal organisation in connection with the same murder between 20 October, 2016 and 22 December 2016.
He is charged with directing the activities of a criminal organisation in connection with the surveillance of James Gately in preparation for the commission of an indictable offence between 17 October 2015 and 6 April 2017.
Another charge alleges that between 20 October and 22 December 2016 he contributed to or participated in activity intending or being reckless as to whether such activity would facilitate a criminal organisation in the murder of Mr Kirwan.
He faces a similar charge of facilitating a criminal organisation in a conspiracy to murder Mr Gately.
