He is developing an English-language, live action version of the long-running French comic, reports Variety.
Launched in 1967, the series is written by Pierre Christin and illustrated by Jean-Claude Mézières.
It follows the adventures of the eponymous time-travelling spatio-temporal agent and his intelligent and beautiful sidekick Laureline.
The Parisian director previously hired Mézières to work on the design of his sci-fi blockbuster The Fifth Element.
Besson is already working on the Robert De Niro, Michelle Pfeiffer and Tommy Lee Jones-starring Malavita and an untitled action thriller starring Angelina Jolie, which is scheduled to begin shooting in early 2013.
The Valerian project's title and timetable are yet to be revealed.