The GMB union said thousands of its members would vote over the next few weeks on whether to launch a campaign of industrial action.
The union said strikes would bring Heathrow, Gatwick and other major airports to a halt "almost instantly".
Talks between the airline and unions representing baggage handlers, check-in staff and other workers have failed to break the deadlock.
National officer Allan Black said: "The GMB deeply regrets the position we find ourselves in - contemplating strike action at the peak of the holiday season.
"We ask the public to understand that this is an action on behalf of thousands of low-paid workers, many of them working part-time and balancing demanding carer responsibilities."
However, BA maintained that the talks had been adjourned until next week. A spokeswoman said: "We would be extremely disappointed if the GMB has decided to ballot its members, particularly given our ongoing efforts to work alongside Acas and the unions to find a resolution."
The GMB said the results of the ballot would be known by mid August.
"It comes after six months of negotiations towards a settlement with BA," Mr Black said.
"Our efforts have managed to produce an offer of 2.5% for 2004, effectively a pay standstill in real terms. That would be followed by more of the same for 2005 and 2006. This is at a time when the fat cats who manage BA are awarding themselves 5.6% rises upon already obese salaries."
