A federal mediator was unable to broker an agreement after meeting both sides on Tuesday, the AP reported, citing Gary Quick, the chairman of the union's negotiating committee.
"We're out picketing now" at the company's Huntington Beach plant, he told the AP.
A Boeing spokesman did not immediately return a message left on his cell phone, the AP said.
The strike could affect satellite launch facilities operated by Boeing's Integrated Defence Systems unit at Vandenberg Air Force Base in California and Cape Canaveral in Florida, the AP reported.