The union, which asked the company to begin negotiations, is attempting to win back concessions made during the airline's Chapter 11 reorganization, which began in 2002 and ended in 2006, Crain's Business Journal reported.
"We are after a complete, fair and equitable contract," Steve Wallach, chairman of the pilots' union, wrote to members Wednesday, the report said.
The airline is "focused on making the right decisions for the future of our company in the face of $110 fuel," a company spokeswoman said.
Industry analyst Robert W. Mann said the union's timing is not ideal, however.
"The airline industry has been battered recently with escalating fuel costs and grounded planes due to maintenance issues," Mann said.