Teller would play Mr. Fantastic in the latest big-screen adaptation of the comic-book series, while Mara would play Invisible Girl, Jordan would play Human Torch and Bell would play The Thing, the entertainment industry trade newspaper said.
Josh Trank is to direct the as-yet-untitled superhero ensemble picture, set for a 2015 theatrical release.
"Fantastic Four" was released in 2005 and was followed by the 2007 sequel "Fantastic Four: Rise of the Silver Surfer." Those films starred Ioan Gruffudd, Jessica Alba, Chris Evans and Michael Chiklis.