Sony wants the Chronicle director to helm its The Amazing Spider-Man spinoff movie, reports the Los Angeles Times.
The villainous alien symbiote that possesses hapless photographer Eddie Brock was played by Topher Grace in Spider-Man 3.
The film has been in the pipeline for some time.
Topher previously revealed that he was not in line to reprise his role in the movie.
There have also been rumours that Brian Michael Bendis turned down the opportunity to write the Venom film.
This Venom project is said to be unconnected to previous drafts.
The Andrew Garfield and Emma Stone-starring Amazing Spider-Man will arrive in cinemas on July 3.
Watch the Amazing Spider-Man trailer below: