The vote was near-unanimous — with 99.4 per cent of the workers voting in favour — giving union leaders in the Association of Professional Flight Attendants authority to call for the strike if negotiations falter.
American Airlines told KERA News that the company and the labour organisation were making progress toward an agreement.
"We understand that a strike authorization vote is one of the important ways flight attendants express their desire to get a deal done," the carrier wrote. "The results don’t change our commitment or distract us from working expeditiously to reach an agreement."
Both sides would have to bring the contract dispute before the National Mediation Board before a strike could go into effect.
Workers have been holding informational pickets around the country during negotiations, including at the Dallas-Fort Worth International Airport. Picketers held signs claiming they were "ready to strike" and bearing the slogan "More Work Less Pay: It's the AA Way."
Workers at airports in Boston, Charlotte, Washington, La Guardia, Orlando, Miami, Las Vegas, Philadelphia and Chicago also picketed.
The company reached an agreement with its pilot last week on a tentative four-year contract. That contract will give the 15,000 pilots in the union a 21 per cent raise on average along with a 401(k) contribution increase and annual pay rate increases.