Lawyers for Ian Bailey want the High Court to rehear his challenge to his extradition to France, in light of new information received from the State.
The High Court ruled that Mr Bailey should be extradited. He is wanted in France for questioning about the killing of Sophie Toscan du Plantier in December 1996.
Mr Bailey appealed that decision to the Supreme Court. Last month the Supreme Court was told new information had been revealed in documents provided to Mr Bailey's legal team by the State.
His lawyers told Chief Justice Susan Denham today that they want "some issues" to be reheard in the High Court.
Lawyers for the State said they do not know what the arguments to be raised by Mr Bailey's team are.
The matter is to be returned to the Supreme Court on 15 December, when Mrs Justice Denham will consider the motion filed and any response filed by the State.
She said the court will then consider whether the motion will go ahead next Friday.
Mr Bailey, 53, is wanted for questioning by an investigating judge in France in connection with the murder of Ms Toscan du Plantier.
The body of the 39-year-old French film maker was discovered near her holiday home in Schull, Co Cork, on 23 December 1996. Mr Bailey has always denied any involvement in the murder.
He was arrested by investigating gardaí and the Director of Public Prosecutions found no basis to charge him.
His appeal against the extradition order had been scheduled to take place last month, but was adjourned because of "highly relevant" new material provided to Mr Bailey's lawyers by the State.
Last week, a new date for the appeal was set for 16 January, but Mr Bailey's team is now seeking to have the matter returned to the High Court.
Mr Bailey's lawyers previously told the court they had received material from the State which was "highly relevant" to his bid to prevent his extradition to France.
They said the material discloses a "breathtaking" level of wrongdoing by State officials.
If this material had been available for Mr Bailey's unsuccessful High Court challenge to the warrant for his extradition, his team would have been able to make "a much stronger case" in that court concerning allegations of garda misbehaviour in the murder investigation, Martin Giblin, Senior Counsel for Mr Bailey, said.
