"The Punisher" star is in negotiations to play Dave Scott, who walked on the moon in July 1971 as part of Apollo 15, making him one of only a dozen men to have set foot on its surface, The Hollywood Reporter said.
Bernthal is joining Ryan Gosling in the biopic, which will reunite the latter with his "La La Land" director Damien Chazelle.
The cast also includes Kyle Chandler, Corey Stoll and Jason Clarke.
Filming is expected to begin this November in Atlanta. The film is set for an October 12, 2018 release in US theatres.