Washington (CNN) Boeing's proposal to bring back the 737 Max has included a computer-based training program that, like requirements before two crashes involving the aircraft, does not involve hands-on simulator training before allowing pilots to resume flying the troubled aircraft once it is no longer grounded, CNN has learned.

Following the crashes involving Lion Air and Ethiopian Airlines in October and March in which 346 people died, some pilots and aviation consultants criticized Boeing for the aircraft's training requirements that previously involved a short, self-administered online course and no simulator time.

While the Federal Aviation Administration has not yet announced any decisions on final training requirements, Boeing's training proposal for the aircraft's updated software included computer lessons without mandated simulator training, according to a pilots' union and a source familiar with the discussions. The training proposal has not been previously reported.

The proposal to require only computer-based training could save airlines money and time when the FAA lifts flight restrictions on the Boeing-made aircraft. When the 737 Max initially went into service, as a selling point, Boeing told airlines it was similar enough to previous versions of the aircraft that they could avoid more extensive simulator training, CNN previously reported

A full-flight simulator can range in price from roughly $6 million to $15 million and can cost hundreds of dollars per hour to use, according to a spokesperson for CAE, a simulator manufacturer that has sold 737 Max simulators to airlines.

Dennis Tajer, spokesperson for the Allied Pilots Association, which represents American Airlines pilots, said some pilots in his group found Boeing's draft training materials to be "inadequate."

Tajer said his group believed Boeing's proposed training materials related to the plane's MCAS system, which is designed to push the nose of the airplane down if it senses an imminent stall and is believed to have played a role in both crashes, needed improvement in terms of presentation and content.

"If you are going to hang your hat on computer-based training, it better be the best of the best if you don't have simulators going with it," Tajer said.

One person familiar with the proposal says pilots on one major US airline could complete re-training its 737 Max pilots in 30 days.

Tajer said the Allied Pilots Association does not oppose additional simulator training if consensus is reached that that should be required, but he said his group remains more concerned about ensuring pilots have the information they need in flight checklists that explain procedures. He said Boeing did provide supplemental training modules that contained informative diagrams his group found "to be quite good."

"We want to tell Boeing that this is a global issue, and we are imploring Boeing not just to provide optionality about how deep the training goes. Tell the FAA what you think should be mandatory," Tajer said.

Mike Trevino, a spokesperson for the Southwest Airlines Pilots Association, told CNN his group does not believe simulator training should be a prerequisite for returning the 737 MAX to service.

A spokesperson for Boeing said the company is in the process of finalizing 737 Max training requirements for submission to the FAA.

The crashes involving Ethiopian Airlines and Lion Air sparked international debate about training requirements for pilots learning to fly updated aircraft models.

In April, an FAA panel concluded in a draft report that simulator-based training is not necessary for pilots who flew the previous version of the 737.

While international regulators met with the FAA in Fort Worth, Texas, last week and discussed training requirements for the 737 MAX, no conclusions about those requirements have been announced.

An FAA spokesperson said in a statement, "Acting FAA Administrator Dan Elwell has said repeatedly that no final decisions have been made on pilot training or modifications to emergency procedures on the Boeing 737 Max. The FAA is focused on the 737 Max and ensuring its safe return to service."

Following the FAA meeting, Canada's director general of civil aviation, Nicholas Robinson, said his agency Transport Canada wants to see Boeing's final training proposal before deciding on whether simulator training should be required.

Paul Hudson, president of FlyersRights, a nonprofit travel-consumer group, told CNN flight restrictions on the 737 Max should not be lifted unless pilots receive additional simulator or in-flight training that involves handling the plane with the updated MCAS system turned off and on.

"Boeing and the FAA said in 2017 this plane was safe. Then after the Lion Air crash in October they said it was safe. Now we should trust them a third time without any real re-training?" Hudson said.