The State has made an application to the High Court to endorse a European arrest warrant received from France for the extradition of Ian Bailey.
The French authorities want to question Mr Bailey in connection with their investigation into the murder of Sophie Toscan du Plantier.
The body of the 39-year-old film producer was found outside her holiday home in Toormore near Schull in Co Cork in December 1996.
Mr Bailey, a former journalist, who is now in his final year of a law degree at UCC, was arrested and questioned twice by gardaí in 1997 and 1998.
The inquiry headed by a French judge was established after the Director of Public Prosecutions decided that no charges be preferred in Ireland against Mr Bailey who has always said he is innocent of any involvement in the crime.
Mr Justice Michael Peart reserved his decision on endorsing the warrant.
The warrant cannot be acted on until it has been endorsed by the High Court.
