The DPP is seeking a dismissal because there are no new or "newly discovered" facts about his case and because it is an abuse of process.
Meehan, formerly with an address in Crumlin, Dublin, but still serving his sentence in Portlaoise Prison, says he has always protested his innocence of the murder and he says there are substantial grounds for his proceedings.
He contends "new facts" emanating from material disclosed for the 2001 trial of John Gilligan show Meehan's 1999 conviction was a miscarriage of justice. Gilligan was convicted on drugs charges and remains in prison.
Meehan alleges the material undermines the evidence of protected witness Russell Warren which was central to the Special Criminal Court's decision to convict him in 1999.
He also claims new evidence shows the trial court incorrectly assessed the level of phone contact between Warren and a phone registered to Meehan on June 26, 1996, the day of the murder.
If certain material was provided to his lawyers for his trial, as gardai are insisting it was, he could not understand why it was not acted upon, he said. His former lawyers may not have realised the significance of it, he added.
He also wants orders requiring the DPP to disclose material related to what he claims is a continuing Garda investigation into the murder of Ms Guerin.
Meehan is serving a life sentence after being convicted of the murder in July 1999 following a 31-day trial before the non-jury Special Criminal Court.
He was also jailed on drugs and firearms charges.
During the trial, the prosecution alleged Meehan drove a motorbike up to the side of Ms Guerin's car on the Naas road and a pillion passenger on the bike fired a number of shots at Ms Guerin, resulting in her death.
Meehan contends, some time after his conviction, he became aware, from material disclosed to Gilligan before his trial, of a number of persons who witnessed the shooting and were interviewed by gardai.
He claims he was not aware of those people, they were not part of the Book of Evidence in his case and his trial legal team had not brought the contents of the statements to his attention.
This material, he contends, was critical to his defence. He also claims he only became aware after his trial that "critical" identification evidence was not brought to his attention during the trial.
Meehan claims the evidence of Marion Finnegan at his trial supported the evidence of Russell Warren and the SCC relied on Warren's evidence to convict him.
He says he learned from the disclosure made to Gilligan before Gilligan's trial, but after Meehan's conviction, Ms Finnegan failed to pick Warren out during a formal identification parade.
Meehan said he instructed new lawyers but they later informed him it was not possible, due to a Supreme Court judgment of March 2006, to rely upon the material emanating from the Gilligan disclosure for Meehan's appeal against conviction, which was dismissed in 2006.
Meehan said he was very unhappy with that. After his appeal, he contacted another solicitor who undertook to prepare an application to have his conviction declared a miscarriage of justice but that application was delayed and he later instructed other solicitors.