The company said federal law required it to inform workers that might lose their jobs. However, "far fewer people will be laid off than what we anticipated last February," airline spokesman Bruce Hicks said.
The airline had been expecting to cut 8,500 jobs, the Fort Worth (Texas) Star-Telegram reported Wednesday.
The airline is required by federal law to send WARN notices to employees that could be laid off and the number that fit the definition categorically came to 11,159, the newspaper said.
The airline has offered workers a buyout program, offering $12,500 or more in severance pay to Transport Workers Union employees with higher compensation paid to workers with longer employment records.
About 1,000 workers have taken the airline up on the offer. The workers have until Sept. 25 to sign up for the buyout program.
Hicks said pilots were not among those sent layoff notices, because a federal law requiring retirement at age 65 begin in December and that will trim pilot numbers low enough to match restructuring plans.