The current chair of the Labour Court, Kevin Foley, has agreed to mediate in the dispute involving Debenhams and its employees.
This was confirmed tonight by Taoiseach Micheál Martin and Tánaiste Leo Varadkar.
The Government is "appealing to all sides to make every effort to resolve this ongoing dispute".
Earlier, Minister of State Damien English said there was no evidence to suggest that implementing the 2016 Duffy-Cahill expert group report into the closure of Clerys would have assisted 1,000 former Debenhams Ireland workers who lost their jobs last April.
Campaigners for the workers argue that had the Duffy-Cahill recommendations been implemented, they could have boosted the right of Debenhams employees to secure the enhanced redundancy entitlements provided for in a collective agreement pre-dating the collapse of the company.
Minister of State at the Department of Enterprise Trade and Employment, Damien English, addressed the issue at an Oireachtas Committee today.
He told the Enterprise Trade and Employment Committee that the Duffy-Cahill report had a narrow focus, based on a situation where assets were separated.
He noted that the authors, Senior Counsel Neasa Cahill and former Labour Court chairman Kevin Duffy, had not established a link to Debenhams.
The Minister said he had seen no evidence to support the claim that implementation of the report would resolve the difficulties currently facing the former Debenhams employees.
"In relation to resolving Debenhams, the State can get involved under the law only so far in this situation, it is a private matter, with a private company," Mr English said.
"My heart goes out to all those workers and I have engaged and met with them. And it is important the State steps in for its responsibilities, and it has done that," the Minister said.
He confirmed that his Department has set up a process to examine the situation which he hopes will conclude next month.
Issues being examined include employees' access to information on the company's financial situation, their rights as creditors, transfers of assets, consultation periods, and the treatment of collective agreements in insolvencies.
The Department is also assessing the establishment of a stand-alone fund to handle ex gratia redundancy payments, but the Minister pointed to issues to be teased out, including who would pay into it or could claim from it.
However, Mr English cautioned that there were no quick or easy solutions.
He highlighted different kinds of redundancies in different corporate contexts: "Some redundancies are about securing the company's survival while others, unfortunately, happen in the context of the company closing its doors for good."
He also told the committee that the Department's legal advice was that it would not be possible to ensure that any new legislation would be retrospective to assist the Debenhams workers.
RISE TD Paul Murphy and Sinn Féin spokeperson on Enterprise, Trade and Employment Louise O'Reilly accused the Minister and the Government of displaying a complete lack of urgency on implementing the Duffy- Cahill recommendations.
Debenhams Ireland went into liquidation in March, and since then, workers belonging to the Mandate trade union have been picketing its 11 stores, preventing liquidators KPMG from removing stock to progress the insolvency.
They argue that the proceeds of the stock should be ring-fenced to fund enhanced redundancy terms of four weeks per year of service provided for in a 2016 collective agreement, rather than the statutory minimum of two weeks capped at €600 per week.
However, the liquidators, Andrew O'Leary and Kieran Wallace of KPMG, insist that the workers are only legally entitled to statutory redundancy, and that preferential creditors like the Revenue Commissioners have first priority on the proceeds of the liquidation.
They have also warned that the liquidation will run out of money before Christmas due to the inability to remove the stock from the stores, adding that this could leave all creditors with little or nothing.