The pilots voted "overwhelmingly" in favour of industrial action, but talks are planned to try to resolve the row, said Balpa.
In a ballot which closed today 96 per cent voted for some form of industrial action on a turnout of 88 per cent, Balpa general secretary Brian Strutton said today.
"Balpa has now received a last minute offer from Easyjet to resolve the dispute and we will consider this carefully in meetings tomorrow before taking any further decisions," he added
"For clarity that means there are no plans for pilots taking industrial action in Easyjet at this stage. We will issue further information tomorrow.”
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. Easyjet can reassure its passengers that no industrial action is currently planned by its UK pilots.”
Balpa said last month that Easyjet pilots were considering strike action because of the dispute with the company's management over rising levels of fatigue, which the union said gave rise to "serious health and safety concerns".