The Quinns will return to the High Court next Thursday, when Ms Justice Elizabeth Dunne will review compliance matters arising out of contempt of court convictions against Sean Snr, Sean Jnr and Peter Darragh Quinn who is evading arrest by remaining out of the jurisdiction.
Sean Quinn Snr faces the prospect of jail if Ms Justice Dunne finds that he has not complied with court orders.
Sean Jnr faces the possibility of being returned to prison, while a warrant is outstanding for Peter Darragh.
Last week the High Court was told by the bank that "nothing" had been done to reverse the breaches since the contempt findings.
The family claims it desisted in its asset-stripping scheme once told to do so last year by the High Court.
It has taken a case where it is claiming it does not owe IBRC Ä2.8 billion as claimed because the debts are tainted by illegality as a result of being part of a share support scheme.
This case may be heard next year.
The family has an undisputed debt of Ä450 million with the bank.
Yesterday (Tuesday) the detailed judgment from the Supreme Court case taken by Sean Jnr against this jailing for contempt was released.
Four out of five Supreme Court judges found that the High Court was entitled to jail Seán Quinn jnr for three months over "outrageous" contempt of court orders restraining the stripping of assets from the Quinn's international property group.
All five judges, however, found that Irish Bank Resolution Corporation, the former Anglo Irish Bank, engaged in "procedurally and substantively flawed" actions seeking to have Quinn jnr jailed indefinitely pending reversal of some 30 asset-stripping measures, when the finding of contempt against him related to just one measure.
While that did not mean the bank did not have strong grounds for pursuing Quinn jnr over the other matters, it must follow "appropriate procedures" and had not done so, Mr Justice Niall Fennelly said.
Mr Justice Adrian Hardiman said some of the difficulties in the High Court appeared to arise from confusion between civil and criminal contempt. Irish law on contempt of court is "amorphous" and it is "most unfortunate" it remains unreformed some 20 years after the Law Reform Commission urged reform, he observed.
Yesterday, giving the Supreme Court majority judgment, Mr Justice Fennelly said there was "ample" evidence to justify the finding of "outrageous" contempt "beyond reasonable doubt" against Quinn jnr via his involvement in the Puga payment.
Ms Justice Dunne jailed Quinn jnr for three months over the Puga payment only and was "amply justified" in doing so, he said.
The Chief Justice, Mrs Justice Susan Denham, Mr Justice Donal O'Donnell and Mr Justice Liam McKechnie all agreed with those findings.
Mr Justice Hardiman dissented but agreed with the majority that the High Court was not entitled to jail Quinn jnr indefinitely to try to enforce compliance with some 30 coercive orders.
Mr Justice Hardiman also said the Quinn family and Anglo Irish Bank have questions to answer in litigation being fought with "extraordinary bitterness" by both sides.
He said that each side considered that the other had perpetrated "grave injustices" against it.
He said the bank believed the family had failed to pay its debts and had thereby added to its difficulties.
The Quinns, he said, "consider that Anglo has ruined them by treating them in a cynical and manipulative fashion, and in particular by inducing certain of them to borrow money for the purpose of attempting to prop up the Anglo share price by the purchase of its shares, when the latter were in, or approaching, free fall".
The judge, in a written judgment by the Supreme Court published yesterday, noted that there were criminal proceedings outstanding over some aspects of the bank's dealings with the Quinns.
The bank has taken a case alleging the family has conspired to asset-strip an international property group worth hundreds of millions of euro over which the bank has security.
Mr Justice Hardiman said Anglo and the Quinn family businesses had been stars of the Celtic Tiger. The then government's guarantee of Anglo and the other banks in September 2008 was likely to dominate the Irish economy for years to come, he said. The Quinn group had also collapsed, with administrators and receivers appointed to it.