Despite ballot closing on February 22
Unite has vowed that any strike action will not be called over the Easter holiday.
Len McCluskey, the union's assistant general secretary, said: "It was never the intention of Unite and its BA cabin crew membership to call industrial action over Easter.
"I want to make it abundantly clear that, if industrial action receives the required mandate from the members and strike action is made necessary by continuing management intransigence, we will not call such action over the Easter holiday period."
But BA said the possible strike is still "threatening the travel plans" of business travellers from March 1, according to Unite's ballot timetable.
"Assurances about an unspecified Easter holiday period will be of little comfort to them," said the airline.
The 12,000 BA cabin crew members of Unite will vote from January 25 on whether to take strike action.
A decision will be made on February 22.
Unite said: "It remains our hope that this dispute can be resolved through negotiation, without the need for strikes at any time at all.
"But this can only happen is BA management wake up and realise that treating their greatest asset - skilled and professional employees - as enemies is the road to ruin. You can't fly planes on management machismo."
www.ba.com www.unitetheunion.org