A spokesman for Fórsa trade union is calling for a third party to become involved in talks between Ryanair and its pilots.
Bernard Harbor says it would be useful to have a third party involved as negotiations were difficult given that for 30 years both parties "haven't sat at the negotiating table".
He told RTÉ's Morning Ireland that "a small number of hours" were needed in talks "to get under the bonnet of issues".
Mr Harbor said that strikes were not good for the airline, their staff, the public or the economy.
A third strike for Ryanair pilots is set for next Tuesday. The airline is also cancelling 600 of a total of more than 5,000 flights between Wednesday and Thursday of next week when Spanish, Portuguese and Belgian cabin crews will strike.
Ryanair wants to continue discussions and the suspension of all strikes. The airline has cancelled 24 flights between Ireland and Britain on Friday and is offering alternatives to the 4,000 customers affected. It is maintaining services to holiday destinations in Europe.
Cabin crew strikes
The airline has also cancelled 300 flights in Europe – not Ireland – on both Wednesday and Thursday of next week ahead of cabin crew strikes. Up to 50,000 of Ryanair’s 430,000 customers (12 per cent) on each of the two days will be hit.
Mr Harbor said that the issue was about working conditions not pay, specifically the transferring of pilots between bases. Pilots want this to be done in a fair and transparent way.
Up until now pilots have been “told by diktat” where they are being sent, Mr Harbor said they want a fairer and more transparent methodology, a change that will not come at a huge cost, he said.
Fórsa will need to see some movement of substance before they will remove the threat of industrial action, he added.