Lawyers for IBRC have asked the High Court to impose a raft of coercive orders against Sean Quinn to rectify his "blatant" contempt of court.
The bank's legal team has not expressly asked for the bankrupt businessman to be jailed, but has suggested the court may consider a punitive element to protect the administration of justice.
IBRC senior counsel Paul Gallagher has described the contempt as a "deliberate and blatant plan to subvert a court order".
The order in question was imposed last summer to restrain the Quinns from moving international property assets beyond the reach of the former Anglo Irish Bank.
Ms Justice Elizabeth Dunne has found it was breached by Sean Quinn, his son Sean and nephew Peter Quinn.
Mr Gallagher for IBRC is now seeking a raft of orders to remedy the situation and has expressed fresh concern about share dealings and rental income from the Quinn's IPG assets, including the Kutuzoff tower in Russia.
Far-reaching disclosure orders are being requested and he has told the court it has the power to make additional policing orders.
Senior Counsel Bill Shipsey for the Quinns is arguing against the reliefs and has called them "most extraordinary and draconian".