This afternoon, Ryanair released a statement saying that have offered to meet with IMPACT members on Tuesday, a day before the proposed strike.
The carrier has agreed to recognise unions for the first time.
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.
Ryanair pilots were planning strike action for Wednesday but it has been suspended.
The Portuguese pilot union has requested a meeting and Ryanair has offered to meet them on Thursday December 21st.
The pilots had backed industrial action by a margin of 94 per cent to six per cent in secret ballots.
Investors in Ryanair have questioned if Michael O'Leary's reign is coming to an end after he yesterday offered to recognise unions for the first time in the company's 32-year history.
It said it would "not engage with pilots who fly for competitor airlines in Ireland or elsewhere".
The Irish Travel Agents Association has welcomed signs of progress towards breaking the deadlock between Ryanair and the IMPACT trade union over the threatened strike by some pilots next Wednesday.
Pilots in Germany have voted to take industrial action during the Christmas period and German union Vereinigung Cockpit said the onus was now on Ryanair to "prove that this announcement is serious".
"Union meetings planned next week and January".
Ryanair, Europe's second-largest airline by passenger numbers, has been forced to cancel 20,000 flights through to March because of pilot scheduling problems stretching back to September.