Reports say that there is space for one other person on the flight, suggesting that another cast member may join them on the journey.
The film was first announced in May, when Nasa administrator Jim Bridenstine tweeted that he was “excited” to work with Cruise on the project.
“We need popular media to inspire a new generation of engineers and scientists to make @NASA’s ambitious plans a reality,” he wrote, with Musk replying that the process “should be a lot of fun”.
As well as directing, Liman is said to be writing the script, with Deadline reporting in July that Universal Pictures have pledged an estimated $200m (£157m) to the production.
So its confirmed that @CommanderMLA is flying the @Axiom_Space @SpaceX #CrewDragon tourist mission with Director @DougLiman & Tom Cruise. One seat still to be filled. They are to launch in October, 2021. pic.twitter.com/dn6SLvCOGz
— Space Shuttle Almanac (@ShuttleAlmanac) September 19, 2020
If the trip goes ahead, it will be the first narrative feature ever to be filmed in space.