Dominic Óg McGlinchey, of Tuam, Co Galway, had brought proceedings against Co Louth coroner Ronan Mcguire over an alleged failure to furnish any documents and files relating to the 1996 inquest into the death.
McGlinchey Snr was shot dead when making a call from a phone box in Drogheda on February 10, 1994, a year after he had been released from prison.
His murder remains unsolved.
The jury at the November 1996 inquest returned a verdict in accordance with the medical evidence, that he died because of bullet wounds to his head.
Following the inquest, the McGlinchey family questioned the Garda investigation into the killing and claimed that two members of the loyalist terror group, the Ulster Volunteer Force (UVF), were responsible.
Earlier this year, Mr McGlinchey Jnr’s solicitor, Ciaran Mulholland, wrote to the coroner requesting to be provided with documents and material that were before the inquest.
It is understood that the material is being sought so the family can assess what reviews of the murder investigation have been undertaken by the gardai.
Some of the material sought by Mr McGlinchey includes depositions to the inquest from the late State Pathologist Dr John Harbison, who carried out a post-mortem examination on the applicant's father.
Other material relates to records of the verdict and depositions given by Mr McGlinchey Jnr, who was aged 16 years at the time of the killing, and depositions of a garda who attended the scene of the 1994 shooting.
The requests for the material in question were not answered by the coroner, it was claimed.
Mr McGlinchey had claimed that under the 1962 Coroner's Act Mr McGuire had a duty to permanently preserve certain documents relating to an inquest.
It is also claimed the coroner has a duty under the 1962 Act to furnish these documents after a person such as Mr McGlinchey has applied for them.
The action was initiated last April after Mr McGlinchey's claims his repeated requests to the coroner to be provided with the material were not answered.
When the case was briefly mentioned before Mr Justice Charles Meenan on Monday, Ronan Munroe SC for Mr McGlinchey said that the coroner has indicated in correspondence that he will provide the applicant with all the material he has in his possession.
"This hopefully, may resolve the matter," counsel said.
However, it was not known at this stage how much of the material sought by his client is in the possession of the coroner, the court also heard.
Mr Justice Meenan said that given the coroner's position he was not prepared to grant the applicant permission to bring the judicial review challenge.
The judge said he was prepared to put the coroner on notice of the application and adjourned the proceedings to a date in July.
Arising out the alleged failure to provide the material sought Mr McGlinchey Jnr sought a declaration that the coroner had failed to comply with a statutory obligation to furnish the relevant documents and that there had been a failure to give any reasons for the alleged failure to comply.
In the mid-1980s McGlinchey Snr became the chief of staff of the Irish National Liberation Army, a group that splintered from the Provisional IRA in the 1970s, after he fell out with them.
The Co Derry native, who was nicknamed 'Mad Dog', led the INLA at a time when dozens of killings and acts of violence were committed during the Troubles.
Neither McGlinchey Snr's murder nor that of his wife Mary, who was shot dead in her Dundalk home in January 1987 as she bathed the couple's children, has ever been solved.