It has been revealed that an estimated 15,000 of the company's flights scheduled to run over the festive period do not have an assigned pilot due to a computer glitch.
The software error gave time off to too many pilots between 17-31 December, the company told employees in an email last week.
Pilots are now being offered more money to cancel their holiday plans and work the shifts.
A US-based aviation union called the incident a “crisis”.
In a statement, American Airlines said: "We are working diligently to address the issue and expect to avoid cancellations this holiday season.
"We have reserve pilots to help cover flying in December, and we are paying pilots who pick up certain open trips 150% of their hourly rate."
The Allied Pilots Association, which represents commercial pilots, said it had not yet heard from American Airlines management about solving the issue.
"I‘m watching a ‘Grinch that stole Christmas’ thing happening,” a spokesman told Reuters.
"And we don’t want to see that happening for our passengers.”
Photo copyright: GETTY IMAGES. Caption: American Airlines is offering pilots more money to come back and work at Christmas