Patricia Quinn and her five adult children have claimed that the liquidation of IBRC was invalid and have sued Kieran Wallace over his appointment as special liquidator to IBRC.
On Wednesday, the High Court agreed that the case may be suitable for resolution through mediation.
Any settlement of this case could open the prospect of resolving all the litigation involving the Quinn family and the €2.34 billion in loans Anglo Irish provided Seán Quinn over seven years ago.
IBRC is suing members of the Quinn family for allegedly putting beyond reach certain international property assets.
The Quinn family members are also suing the Department of Finance and the Financial Regulator and named former Anglo Irish directors.
That case has been put on hold by the High Court until next year.
The delay has now opened a window of at least seven months to see if mediation will work, sources said.
The costs of the case for both sides are immense.
It is understood that the Quinn family is now hopeful that the appointment of a mediator and a successful deal between the two parties could lead to the settlement of the huge legal disputes between the family and the State.
“It could be the breakthrough. They don’t know,” said a source. “They are looking at a mediator either by a SC or a retired judge. Could an IBRC settlement lead to settlement of the other cases? Could the Department of Finance come into it? They do not know.
“They are keeping a very open mind on the matter. If the mediation ends up solving one part of the problem — that’s just fine.
“If the mediation is gone into in good faith, which they have no reason to believe it has not, they could say it would be wrong to rule out all potential cases. That is not on the table at the moment, but one has to assume that that is a possibility.”
Speculation first surfaced late last summer that the sides were moving closer to some sort of settlement, but this was denied by Quinn family sources.
The prospect for mediation was first reported earlier this year, but a potential settlement appeared to have been scuppered in recent weeks,with reports that the deal had stalled.