The group of unions at Aer Lingus will meet the Minister for Transport, Mr Cullen, tomorrow to discuss the future the airline.
The meeting is the start of a process agreed at Cabinet yesterday, in which Mr Cullen will meet the stakeholders at the company before reporting back at the end of January.
There have been ongoing industrial relations difficulties at the company over plans make over 3,000 workers redundant as part of a move by the airline to a low-cost model.
Mr Cullen will also be investigating methods of financing with the company needing up to €1 billion by 2008 to buy new planes.
Unions are concerned about suggestions that the airline may be privatised and following the Budget earlier this month, ICTU president, Mr David Begg expressed disappointment that there was no new investment in Aer Lingus announced.
Yesterday's decision to defer a decision on future funding until the new year was by Fine Gael as another "broken promise".
Ms Olivia Mitchell said the failure to make a decision condemned the airline and its staff to further uncertainty. "Uncertainty in the airline business can be terminal. It is impossible to run a business in such a volatile industry without a clear strategic plan, a confirmed budget and a motivated management team," she said.