A House aviation panel is scheduled to hear from pilots, flight attendants and airline representatives at its second hearing about the plane, which has been grounded worldwide since mid-March after two fatal crashes within five months of one another killed a total of 346 people.
Boeing is scrambling to win regulators' approval to get the 737 Max, its best-selling aircraft ever, flying again and to win back public trust after several surveys showed travelers might try to avoid the plane.
Dan Carey, president of Allied Pilots Association, which represents some 15,000 American Airlines pilots, plans to tell lawmakers Wednesday that Boeing has "made significant positive changes with the new software fixes," according to written testimony reviewed by CNBC.
"However, at APA we remained concerned about whether the new training protocol, materials and method of instruction suggested by Boeing are adequate to ensure that pilots across the globe flying the MAX fleet can do so in absolute complete safety," he said in his statement.
American Airlines has "been working closely with our pilots on the APA national safety committee on the suggested training and other issues concerning returning the 737 MAX back to revenue service," said American spokesman Ross Feinstein. "We appreciate their input and collaboration."
Boeing has developed a software upgrade for the jets but regulators have yet to sign off on those changes.
Carey also questioned whether the Federal Aviation Administration can ensure that pilots receive enough training "as aircraft are becoming more and more technologically sophisticated."
The union has criticized Boeing for not providing enough information about an automated anti-stall system aboard the 737 Max planes. That system, known as MCAS, has been implicated by investigators in the two crashes. Carey called a lack of training on the system "the final fatal mistake."
Members of the pilot union met with FAA officials earlier this month and discussed training for the aircraft, a spokesman said.
Carey told CNBC the union has requested simulator time in the sole Boeing 737 Max full-motion simulator in the U.S., which is located in Miami, and said American told the union it can receive the simulator time after the plane is certified by the FAA. The pilots previously used a stationary simulator near Boeing's production facility near Seattle.
American ordered a 737 Max simulator that should arrive by the end of the year, Feinstein said.
The Association of Professional Flight Attendants, which represents American's cabin crew and is not testifying in person at Wednesday's hearing, sent testimony to the House panel that says the issue of trust must be addressed before the plane flies again.
"If the public does not believe that the process of returning the 737 Max 8 to service is not the result of a thorough, rigorous, and transparent safety-driven process, then this aircraft will likely be forever tainted," the statement said.
The House panel is also scheduled to hear from Airlines for America, an industry group that represents most of the largest U.S. airlines; the Association of Flight Attendants, which represents United Airlines cabin crew members; and Capt. Chesley "Sully" Sullenberger, famed for his 2009 "Miracle on the Hudson" landing of a US Airways Airbus jet.