Aer Lingus management has invited pilots to talks ahead of a work-to-rule beginning on Wednesday.
244 flights have been cancelled because of the action that will also include a full work stoppage on Saturday.
This includes an additional 120 flights were cancelled at the week after an eight-hour strike was announced.
President of the Irish Airline Pilots Association (IALPA), Captain Mark Tighe, says everything is a possibility, but at this stage they're not considering an all-out strike.
" The company has finally written to us and asked us for a meeting.
"However, they have attached preconditions to that invitation of what we can and only can talk at the meeting.
"So we're discussing their preconditions at the moment, but we see this as a positive.
"I would very much hope that it would happen this week. We've always been, and continue to be, available to meet the company.
"It is the company that hasn't wanted to meet".
Enterprise Minister, Peter Burke, is urging both sides to find a resolution.
"It's so important to our economy. We know that air connectivity is the heartbeat of an open economy, like we have on our island.
"It's so important that this disruption does not impact on thousands of people be it in business, people traveling, our tourism sector, it's a very important time for all of those sectors.
"So we need to ensure that we have urgency attached here".
