Alex Kurtzman is directing the movie, which is set to launch Universal's new monster universe, said The Hollywood Reporter.
Sources say Universal has been looking for a big star to anchor the film, and is hoping Cruise will fill that role. Universal has not commented yet.
The film will be set in present day and is set for release on March 24, 2017.
Jon Spaihts has written the script although plot details are being kept deep in the tomb. Kurtzman, Chris Morgan and Sean Daniel are producing.
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Cruise, 53, was most recently seen in "Mission: Impossible - Rogue Nation".
The reboot will begin shooting mid-February.
Cruise will then head back to the "Mission: Impossible" franchise for the sixth installment, which will shoot in later 2016.
His other upcoming films include "Jack Reacher: Never Go Back" and "Mena".