The jets were grounded worldwide more than a year and a half ago after the two crashes — Lion Air Flight 610 in October 2018 and Ethiopian Airlines Flight 302 in March 2019. All 346 people on board the flights were killed.
Following repeated setbacks, the Federal Aviation Administration is at the tail-end of its recertification process for the jets though it has not signed off on the planes officially.
"The FAA continues to follow a thorough process, not a prescribed timeline, for returning the aircraft to service," it said in a statement.
Boeing has made several changes to the planes' software including making a flight-control system that pilots struggled against in both crashes less aggressive.
"We are seeing that finish line approach us and I think it's a real finish line," David Seymour, American Airlines' chief operating officer, told employees in a town hall meeting last week, which was reviewed by CNBC.
The Fort Worth-based airline has been the most optimistic U.S. carrier about the timeline for the jets' return. American is planning to start 737 Max flights with employees after Thanksgiving, estimating the FAA will lift the flight ban in mid-November, Seymour said. An American Airlines spokesman said the company's plans are tentative, based on the FAA's decision.
American last week said it scheduled what it expects will be the first 737 Max flights since the jet's grounding for some service between New York's LaGuardia Airport and the carrier's Miami hub starting Dec. 29 through Jan. 4.
American is planning offer some customers a chance after Thanksgiving to see the aircraft in person at airports, including Dallas/Fort Worth International Airport, LaGuardia and Miami, with the participation of pilots and mechanics. Pilots can also answer customer questions through calls and video messages, the company said.
"They're the ones that ... really have the credibility to explain the Max," said Alison Taylor, American's chief customer officer, in the employee town hall.
Customers booked on the 737 Max will receive notifications and be able to switch to another flight if they don't feel comfortable, Taylor said.
The union that represents American's pilots cautioned against promoting the jets' return.
"There are 346 reasons to be respectful and not have a PR campaign," said Dennis Tajer, spokesman for the Allied Pilots Association and a Boeing 737 captain. "When the Max is fixed, fully vetted and we've been robustly trained, then it will be time to just go fly the jet."
American's Boeing 737 pilots can sign up for December training sessions, which will include a virtual training that will likely last about an hour and 40 minutes around two hours in a flight simulator, the union told its members last week.
The plane's grounding plunged Boeing into its biggest-ever crisis, which was later compounded by the coronavirus pandemic's toll on air travel.
U.S. airlines alone lost more than $10 billion in the third quarter and carriers around the world have cancelled hundreds of 737 Max planes. American, which had 24 737 Max planes in its fleet at the time of the March 2019 grounding, has an agreement with Boeing that would allow the airline to defer orders of 18 others to as late as 2024.
United Airlines' chief commercial officer Andrew Nocella said earlier this month in an earnings call the airline will put the planes back on its schedule "likely sometime next year based on the schedule we hear from the FAA and Boeing."
Southwest Airlines CEO Gary Kelly last week told CNBC that the airline hasn't scheduled any new Max flights because it still hasn't been cleared to fly. Kelly estimated it could return in the second quarter of 2021, however.
Boeing is scheduled to report third-quarter results before the market opens on Wednesday, when it will detail the financial impact of Covid-19 on aircraft demand and the latest steps in getting the Max flying again.