Boeing's best-selling 737 MAX has been grounded since March, after two deadly crashes in five months killed 346 people.
In a note to pilots on Wednesday, Jon Weaks, head of the Southwest Airlines Pilots Association, said, "Boeing is increasingly publicizing that they may have to shut down their production line due to running out of room to store completed MAX aircraft. There is some concern that this is simply another tactic to push the (return to service) timeline up."
Federal officials told Reuters this week that Boeing's timetable is aggressive and far from certain.
Boeing did not immediately comment to Reuters late Wednesday.
On Friday, Southwest and American Airlines extended Boeing 737 MAX cancellations until early March.
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Last month, SWAPA sued Boeing, saying it had "deliberately misled" the airline and pilots. The grounding wiped out more than 30,000 Southwest Airlines flights, causing over $100 million in lost wages for pilots, the union said.
Weaks said in the note, "Boeing will never, and should not ever, be given the benefit of the doubt again, The combination of arrogance, ignorance and greed should and will haunt Boeing for eternity."
He also supports the idea of Southwest looking to obtain different and possibly non-Boeing aircraft.