The signing will take place on the sidelines of the upcoming Trump-Kim summit, sources told Reuters.
The sources also said Vietjet will finalize next week a provisional deal agreed last year to buy 100 narrow-body Boeing 737 MAX jets worth almost $13 billion at list prices.
The U.S. Federal Aviation Administration (FAA) last week gave Vietnam a Category 1 safety rating, allowing local airlines to operate direct flights to the U.S.
Vietjet, along with other local airlines, had previously expressed interest in operating direct flights to the U.S.
The carrier, the largest private airline in Vietnam, had also signed a deal to buy Boeing 737 MAX narrow-body jets when former U.S. President Barack Obama visited Hanoi in 2016.
It also finalized a deal in November last year with Airbus for 50 A321neo jets during a visit to Hanoi by French Prime Minister Edouard Philippe.
Vietjet currently operates 40 domestic routes and 66 international routes. It has 385 flights daily within Vietnam and to places such as Japan, Hong Kong, South Korea, Taiwan, Singapore, mainland China, Thailand, Myanmar and Malaysia.