The Lion Air crash in Indonesia last October and another accident this month involving an Ethiopian Airlines jet, which killed 346 people between them, have raised major concerns about the safety certification of the 737 MAX 8 model.
A US 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.
An FAA spokesman said Saturday that the agency expects to receive the software fix early next week.
The news comes as Boeing and the FAA are facing a rare safety crisis that has shaken the confidence of global regulators.
Boeing Co said it invited more than 200 airline pilots, technical leaders and regulators for an information session on Wednesday as it looks to return the 737 MAX to commercial service. In a statement, he said pilots were also made aware of an emergency directive issued by the FAA after the Lion Air crash, which killed 189 people.
"Passengers always ask what type of plane they will fly as they have lost trust and confidence in the Max 8 jet", Ikhsan Rosan, a spokesperson for the airline, told The Associated Press.
The two crashes occurred under similar circumstances.
Both crashes are still under investigation.
UNHRC says Israel used 'excessive force' in Gaza
At least 257 Palestinians have been killed by Israeli fire in Gaza since protests began on March 30 2018. The Human Rights Council made the request to U.N.
American said earlier this month it was flying about 85 flights a day out of its 6,700 daily departures on 737 MAX planes when the grounded was announced.
The MCAS is created to account for changes to the plane's engines.
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 in the air again as soon as possible with an acceptable level of safety.
The circumstances under which Boeing designed the plane and the FAA's oversight of it are the subject of numerous lawsuits, congressional inquiries and a criminal investigation.
The meetings are a sign that Boeing's planned software patch is nearing completion, though it would still need regulatory approval. After the update, the system will rely on data from more than one sensor before it automatically pushes the plane's nose lower.
The updated software designed by Boeing uses input from two sensors on the nose of the plane, instead of one, and is created to not trigger the MCAS system repeatedly, which is believed to have pitched the Lion Air plane's nose down so sharply that the pilots' attempts to regain control were futile.
The Wall Street Journal reported Saturday that the system would include new alerts meant to tell the crew when the MCAS is triggered.
Boeing said it was making changes to its flight-control software, known as MCAS, that was created to prevent the aircraft from stalling.