The signing is set for Monday during U.S. President Joe Biden's state visit to Vietnam, an anonymous source told VnExpress.
The deal is part of Vietnam Airlines' plan to renew its fleet, in which many aircraft are over 10 years old.
Four years ago the state-owned carrier received approval from the Civil Aviation Authority of Vietnam to buy 50 narrow-body aircraft from Boeing or its European competitor, Airbus.
Vietnam Airlines and other carriers in the country do not currently use any Boeing narrow-body aircraft.
Vietnam Airlines' 90-jet fleet is made up of the narrow-body Airbus A321 and wide-body Boeing 783 Dreamliner.
The Boeing 737 Max can carry between 210 and 230 passengers and has a range of around 3,000 kilometers.
Budget airline Vietjet signed a deal with Boeing in 2016 to buy 100 737 Max aircraft during former U.S. President Barrack Obama's visit.
It then signed a similar deal in 2018.
Industry insiders say buying new jets is not easy now since Boeing and Airbus have full orders booked for until 2030.