Balpa general secretary Brian Strutton said 96% of a turnout of 88% of union members voted for industrial action.
"Balpa has received a last minute offer from Easyjet to resolve the dispute and we will consider this carefully.
"That means there are no plans for pilots taking industrial action at this stage," said Mr Strutton.
In a statement, the airline said: "Easyjet is committed to working with Balpa to find a resolution to the issues raised and we hope to reach a mutually agreeable solution."
Earlier this month, it was revealed that pilots were considering strike action over the October half-term holidays.
At the time the airline, which has around 2,000 UK-based pilots, said the pilots' workloads were set by the Civil Aviation Authority.
Easyjet operates in more than 30 countries, flying to popular holiday destinations such as France, Italy and Spain.
Easyjet will hold talks with pilots' union Balpa on Thursday in an attempt to resolve a dispute over fatigue and avoid a possible strike.