James Watkins (The Woman in Black) was previously attached to direct the action adventure, with Arash Amel penning the script.
The current draft was written by Zach Dean, and new writers are being sought to polish that script for Rønning and Cruise.
The film will follow Cruise as the legendary 1,000-year-old man, who has used his time on the planet to develop an unparalleled set of survival skills.
According to Deadline, producer David Heyman is attached to star in the title role.