Graham Dwyer is seeking legal aid for his High Court action against the Garda Commissioner and the State over the use of mobile phone records as evidence in his trial.
Dwyer was convicted last year of the murder of Elaine O'Hara in August 2012. He is appealing his conviction but that appeal has not yet been listed for hearing.
He began his High Court action shortly before the murder trial began in January last year. A date for a full hearing has not yet been set.
The court heard this morning that a motion seeking a recommendation from the High Court granting legal aid for the action could be adjourned, with the consent of both sides, to the end of next month.
Mobile phone data played a central part in Dwyer's trial and conviction. The issue of the legislation under which the data was obtained was raised during the murder trial and is likely to form one of the grounds of his appeal.
He claims that the Communications (Retention of Data) Act of 2011 is incompatible with the European Convention on Human Rights, the Constitution and the EU charter of fundamental rights.
In legal argument made in the absence of the jury at his trial, Dwyer's lawyers said the legislation requiring companies to retain data on phone users for two years was introduced following a European Union directive in 2005.
The European Court of Justice found in 2014 that the directive breached the EU charter of fundamental rights and ruled it was illegal.
Dwyer's lawyers claimed this meant the Irish legislation, allowing the retention and use of data collected on his phone activity, was also illegal.
The prosecution argued that the act was a continuation of Irish legislation governing the retention of data.
They also argued that the EU charter only applied to EU law and it did not apply in this instance as the directive no longer existed.
Mr Justice Tony Hunt ruled against Dwyer during the trial and the mobile phone data was admitted as evidence.