And an IALPA official warned the talks may come too late to halt a strike.
Impact said it would meet Ryanair management on Tuesday and "looked forward to establishing a positive relationship".
On Saturday evening Ryanair issued a statement, offering to meet the union and their Ryanair Pilot Committee on Tuesday "if that would suit them better".
The Irish union responded on Sunday that it would be "happy to do that".
The Irish Airline Pilots' Association (IALPA), a branch of the IMPACT trade union, served the airline's management with notice of a one-day strike on December 20, the Wednesday before Christmas weekend, over the airline's refusal to enter direct negotiations with the European Employee Representative Council (EERC) or IALPA as the sole independent representative body for pilots working in the company.
A spokesman added: "Once we meet, we can take a decision on deferring industrial action".
Speaking to RTÉ yesterday morning, Bernard Harbor said the union wanted the meeting to make sure there was substance to the offer Ryanair had made, and to flesh out how the airline's recognition of unions would proceed.
It is the first time Ryanair boss Michael O'Leary has extended such an invitation to union leaders in the 32 years the company has been flying.
It has asked the airline to release its pilot representatives so they can prepare for and attend the meeting.
Pilots in Germany had voted to take industrial action some time during the Christmas period.
In Spain, there are no strikes planned for pilots but ground staff unions have not ruled out action on 30 December.
Some 117 directly-employed Ryanair pilots are involved in the dispute, making up the majority of the firm's captains in Ireland - meaning any walkout would have severely affected flights.
The carrier admitted it had "messed up" the planning of its pilots' holidays.