The High Court has heard that Ian Bailey is expected to apply in August for legal costs following the court's refusal last week to order his extradition to France in relation to the death of Sophie Tuscan du Plantier.
Mr Bailey (60) of The Prairie, Liscaha, Schull, west Cork, denies any involvement in the death of Ms du Plantier, who was found dead outside her holiday home in Schull in December 1996.
French authorities previously sought the surrender of Mr Bailey in 2010 but this application was refused by the Supreme Court in 2012. A second extradition request was transmitted to Ireland last summer, seeking the surrender of Mr Bailey for alleged voluntary homicide.
French authorities have previously prosecuted people for crimes committed against French citizens outside of France. Mr Bailey, who claims gardaí tried to frame him for the killing of Ms du Plantier, could be tried in France in his absence.
Last week, Mr Justice Tony Hunt refused to order the extradition, dismissing the Minister for Justice's application as an "abuse of process", among other reasons.
During today's brief hearing, Mark Thompson BL, counsel for Mr Bailey, told the court that his client, who was excused from the proceedings, wants the matter finalized and that there will be an application in relation to costs.
The matter was adjourned until August 17th.