CHICAGO/WASHINGTON (Reuters) - Teams from the three U.S. airlines that own 737 MAX jets headed to Boeing Co’s factory in Renton, Washington, to review a software upgrade on Saturday, as U.S. regulators prepared to receive and review the fixes in coming weeks.

The factory visits indicated Boeing may be near completing a software patch for its newest 737 following a Lion Air crash that killed 189 people in Indonesia last October. This month, a second deadly crash involving an Ethiopian Airlines MAX in Addis Ababa triggered the fleet’s worldwide grounding.

Timing for when passenger flights will resume remained uncertain. Boeing has come under global scrutiny along with the U.S. Federal Aviation Administration (FAA), the agency that must approve the software fix and new training.

Meanwhile, Southwest Airlines Co, the world’s largest operator of the MAX, began parking its fleet at a facility in Victorville, California, at the southwestern edge of the Mojave Desert, to wait out the global grounding. Southwest has 34 of the jets; United Airlines has 14 and American Airlines has 24.

Acting administrator Dan Elwell told lawmakers last week that the FAA expected Boeing would complete its upgrade as early as March 25, kicking off the approval process.

An FAA spokesman said Saturday that the agency expects to receive the software fix early next week.

A U.S. official briefed on the matter Saturday said the FAA has not yet signed off on the upgrade and training but the goal is to review them in coming weeks and approve them by April.

It remained unclear whether the software upgrade, called “design changes” by the FAA, will resolve concerns stemming from the ongoing investigation into the March 10 Ethiopian Airlines crash, which killed all 157 on board.

The U.S. official said planned changes included 15 minutes of training to help pilots deactivate the anti-stall system known as MCAS in the event of faulty sensor data or other issues. It also included some self-guided instruction, the official added.

The Allied Pilots Association (APA), which represents American Airlines pilots, said it has been in talks with Boeing, the FAA and airlines to get the airplanes flying again as soon as possible with an acceptable level of safety.

“Right now we’re in wait-and-see mode to see what Boeing comes up with,” said Captain Jason Goldberg, spokesman for the APA, part of a delegation of airline safety experts and pilots set to test the upgrade. “We’re hopeful, but at the same time the process can’t be rushed.”

Boeing said on Saturday it was continuing to schedule meetings with all 737 MAX operators.

Southwest and United said they would also review documentation and training associated with Boeing’s updates on Saturday.