The Dáil is set to vote on the sale of the Government's stake in Aer Lingus today.
Further details have emerged about a confidential report prepared for the airline by consultants NYRAS - which reportedly sets out a range of cost reductions including cuts to cabin crew and pilot numbers.
However, Aer Lingus says the report was a cost-base comparison presentation and has no bearing on jobs.
Fianna Fáil is calling for today's vote to be suspended in light of the report.
Transport Spokesperson Timmy Dooley is refusing to accept the airline's claims that the report has nothing to with jobs.
"My understanding is that it recommends an aggressive approach to those cost reductions, with potential savings of around €60m," he said.
"I think if anybody were to do any basic analysis they would know that a €60m reduction in cost will see a reduction in the number of people employed, either directly, or through indirect companies."
Aer Lingus chief executive Steven Kavanagh has moved to reassure the Labour Party about job concerns at the airline.
Mr Kavanagh wrote to Labour Junior Minister Ged Nash last night - stating that the airline has a strong preference to use direct labour wherever this can be done "effectively and efficiently".
He said it is the company's clear preference to avoid compulsory redundancies.