The liquidator of the Debenhams Irish operation KPMG has said another retailer is seeking to reopen a number of the stores, and if successful, it could save hundreds of jobs.
The liquidator has not revealed the name of the retailer or what stores it is interested in reopening.
Former staff have been officially picketing Debenham's 11 Irish stores for a number of months calling for what they describe as a fair redundancy package.
They are angry about how the fashion store has treated employees following the closure of its stores in Dublin, Cork, Limerick, Galway and Waterford earlier this summer.
However, KPMG has said the protests, which are impeding the removal of stock from the stores, need to end to allow Debenhams stock to be removed and the new retailer to move their stocks in.
In a statement, the liquidator said "Mandate agreed this was a good solution and issued an instruction this afternoon to their members to stop the protests".
It also said employees have now started "an unofficial strike in Cork, which is a real threat to jobs being saved".
The Mandate Trade Union, however, has said there are no unofficial protests taking place outside any former Debenham stores, but that official pickets will remain in place "and there is a requirement that the pickets remain lawful".
Gerry Light, General Secretary Designate of Mandate, said, "if there is potential to save jobs, we would welcome that, and would seek an opportunity to engage with the new operator".
He said a meeting of shop stewards took place today, and the possibility of a new retailer taking over the stores was relayed to members, but no instruction was issued to stop the Mandate pickets.