Vic Armstrong has entered negotiations to direct the new adaptation of the book series based around the rapture, according to The Hollywood Reporter.
Tim LaHaye and Jerry Jenkins's bestselling novels centre around a world dealing with the disappearance of all faithful Christians that heralds the beginning of the end of days.
Paul Lalonde, who produced three previous adaptations of the novels with star Kirk Cameron, will return as a producer alongside Michael Walker.
The pair are apparently hoping to launch a trilogy.
Armstrong last directed 1993's Army of One. He most recently worked on the stunts in Salt, Thor and The Amazing Spider-Man.
Cage most recently leant his voice to animated family movie The Croods and is expected to make a cameo in Jeff Wadlow's Kick-Ass 2.
The Left Behind film is to begin shooting in spring 2013.