Liam Dominic Adams is wanted in Northern Ireland in relation 18 alleged offences against Aine Tyrell, who has waived her right to anonymity.
The 56-year-old, who denies the allegations, has fought his extradition from the Republic at the High Court in Dublin.
Mr Justice John Edwards told the packed courtroom he has made a decision on extradition but that it was not “polished”.
“The court has arrived a decision,” the judge said. “I’ve prepared a judgment and I’m conscious the parties will want to consider the judgment because whoever is the losing party might want to appeal to Supreme Court.
“I’m anxious the judgment should be as polished as it could be in the circumstances,” he said. “While the judgment is ready I would prefer to hold it over until Monday in terms of making it available.
“I could indicate the decision and give my reasons on Monday or I could hold everything over until Monday and I will be guided by parties,” said Mr Justice Edwards. “There are time limits involved if certain things were to happen.”
Both Michael O’Higgins, the barrister for Adams, and Aileen Donnelly, senior counsel for the State, indicated they would prefer to wait until Monday.
Ms Tyrell (38), who had travelled from Belfast for the hearing, was visibly upset as she left the Dublin’s courts flanked by family members.
The sex abuse claims became public in December 2009 when Ms Tyrell was featured in a television documentary.
Liam Adams is accused of rape, indecent assault and gross indecency at various addresses in Belfast between March 1977 and March 1983, when his daughter was aged between four and 10.
In an affidavit to the court, Liam Adams said has been prejudiced by the delay in bringing charges and widely condemned as a guilty man by the media and persons of repute and in positions of authority, including his brother.
The High Court was told a complaint was first lodged by Ms Tyrell and her mother, Sarah Adams, to police in Belfast on January 21st, 1987.
Liam Adams, whose last address was Bernagh Avenue in Belfast, denied the allegations when arrested in February 2007. A European arrest warrant was issued almost two years later and he handed himself in to gardaí in Dublin.
The judgment will be delivered in the Criminal Courts of Justice on Monday.