EasyJet pilots are understood to be considering a strike in early October that would coincide with many families' half-term holiday plans.
Around 2,000 pilots based in the UK are being balloted about industrial action by the pilots' union the British Airline Pilots Association (Balpa). The ballot will close on 21 September.
The move towards industrial action has been prompted by a dispute with the company's management over rising levels of fatigue, which unions have said risk "serious health and safety concerns", the Telegraph reported.
"The core issue of the dispute was that fatigue has risen year-on-year, to levels pilots and Balpa find unacceptable," said a letter to pilots from Balpa, leaked to the Telegraph.
If enough pilots vote to move ahead with the strike they are likely to fall in the October half-term holidays, when many families travel overseas.
This would be the first strike in Britain for Sir Stelios Haji-Ioannou's budget airline.
Unions and EasyJet had been in talks for more than a year, though these broke down in August and prompted the current ballot.
In a statement today the airline said:
EasyJet can reassure its passengers that no industrial action is currently planned by its UK pilots. Although Balpa has informed us they are balloting their members, EasyJet and Balpa continue to work together as we are both committed to finding a resolution to the issues raised and we still hope to reach a mutually agreeable solution.