Lawyers for developer Paddy McKillen have asked the Supreme Court to give priority to his appeal.
Mr McKillen is appealing the High Court's dismissal of his challenge to the National Asset Management Agency.
Senior counsel Michael Cush said there was a 'real urgency' about it.
Lawyers for the State said they also wanted to underscore the urgency of the case.
The Chief Justice John Murray said the case would be given appropriate priority.
However, he said the court was in serious difficulties given the complex and detailed cases scheduled for hearing this term.
Mr McKillen will make an application tomorrow in the Supreme Court for a stay on the transfer of his loans to NAMA pending the outcome of the appeal.