The jets were grounded worldwide in March 2019 after two crashes killed 346 people, prompting software and other changes on the aircraft. The Federal Aviation Administration is going through some of the last steps that would allow the planes to fly again but hasn't provided a specific timeline. The FAA last month issued the safety changes needed for the planes to return to service. Public comments on those changes are due Monday.
An American Airlines spokesman said that the company hasn't made any "definitive plans" on the Max and that the pilot training date can be adjusted based on regulators' work.
"With the planned return to service for our B737 MAX aircraft in the near future, we will begin conducting B737 MAX Special Training for our B737 pilots," Ameya Kingaonkar, director of flight training planning and scheduling, said in a pilot memo, which was seen by CNBC.
Kingaonkar said that the company expects to train all of its 737 pilots on the Max by the end of January.
"We are awaiting the FAA's guidance regarding the Max, and that guidance will drive our future timelines," a Southwest spokesman said.
The 737 Max, while fuel-efficient, would return to air travel running at just a fraction of last year's levels because of the coronavirus pandemic. Last week, the Transportation Security Administration screened 4.9 million people at U.S. airports, down about 5% from the previous week and nearly 70% lower than a year ago.
Airline stocks were down sharply on Monday as concerns over possible further Covid-19 restrictions in Europe amid more outbreaks of the virus.
Shares of American Airlines on Monday closed down 7.4%, while Delta lost 9.2% and United fell 8.6%, The S&P 500 ended the day off 1.2%.