Talks aimed at averting next Tuesday's threatened industrial action by Aer Lingus pilots in a row over rosters are continuing.
If the action proceeds, up to 30,000 passengers a day will face significant disruption to flights.
Michael Landers from the IMPACT union has said that differences remain between the two sides.
But he added that both sides were working hard to avert industrial action.
Mr Landers said that both sides had exchanged position papers.
Earlier, the Director of the Labour Relations Commission Kevin Foley has said that both sides in the Aer Lingus dispute are in constructive engagement.
Kevin Foley said he was confident that both parties are committed to working for as long as it takes to explore every possibility for agreement.
He added that there was a complex set of issues to be resolved.
On his way into the talks at the Labour Relations Commission, Aer Lingus Director of Human Resources Michael Grealy said the outlook for passengers next week was looking increasingly serious and the time to find a solution was running out.
He said the company was allowing passengers who are expecting to travel on Tuesday and/or Wednesday to change their bookings online for free.
Meanwhile, Michael Landers from the IMPACT union said there had been constructive talks but that significant problems remained unresolved.
