The new Crew Dragons will not be made by the company and will instead be used to reuse the fleet of four already in existence, according to the report.
If needed, the company will be able to make more of the astronauts capsule, according to the president.
The Crew Dragon is the first crewed spaceship from the company and it borrows its design from the Dragon cargo capsule. Since its debut in 2020, Crew Dragon has taken humans to space in five separate missions.
NASA uses Crew Dragon to shuttle astronauts to and from the International Space Station. NASA ordered three more Crew Dragon missions from the company in February, after they landed the Commercial Crew Transportation Capability (CCtCap) contract for six missions with the agency. The nine separate missions will net the company around $3.5 billion.
The International Space Station has a monopoly on human spaceflight. Boeing's proposed crewed spaceship, Starliner, has been beset by technical delays that have halted even a test flight.
The company still has a lot of work to do on the next-generation launch system. The first flight test of the new spaceship will take place in May, but the company is still awaiting key regulatory approvals from the FAA.