The Labour Relations Commission is expected to issue an invitation to managers and unions at the airline to talks on Saturday and Sunday in a bid to prevent a stoppage at the airline on Tuesday.
Earlier, Aer Lingus described the current row with its pilots as a 'watershed dispute'.
Commercial Director Enda Corneille said that the company fully intends to operate a full service next Tuesday, which is the deadline for suspending pilots who refuse to co-operate with the establishment of the airline's new base in Belfast.
However, he said that whether it can do that is in the hands of the pilots, depending on whether they agree to carry out their duties.
The dispute escalated further today, with the suspension of two more pilots.
This brings to seven the number of pilots who have been suspended for refusing to carry out certain duties relating to the recruitment, training and assessment of new pilots.
Mr Corneille said that so far the airline has not put contingency arrangements in place, but that by Monday it will be in a position to assess what alternative plans may be required.
He said he hoped sense would prevail and that the pilots would carry out their full duties.
Mr Corneille said the dispute was about the company managing the business, rather than a union carrying out an effective veto on change.
He said they had engaged with pilots for months but had reached the point where there had been enough talking.
Asked whether they were prepared to close the airline, Mr Corneille said they have to win this battle, as the issue is fundamental to the future of the airline.
