The High Court will rule later today whether RTE can broadcast a news report about Denis O'Brien's banking arrangements with IBRC.
The businessman is trying to stop details of his confidential loan arrangements going public.
RTE said its report looks at the governance of IBRC amid concerns about the bailed-out bank's handling of large debtors, one of whom was Denis O'Brien.
The story relates to a letter the businessman sent in 2013 to the bank's special liquidator, Kieran Wallace, about the terms of his loan facilities.
There is no allegation of wrongdoing against Mr O'Brien, but he claims revelations about his private banking will damage him commercially and may cause him to review his arrangements with Irish banks.
RTE's lawyers called it a threat and said Mr O'Brien "should find some other horses to frighten".
Mr Justice Donald Binchy will rule on the injunction application this afternoon.