According to Radar online, the 52-year-old actor has offered the "Paper Towns" actress the film.
"Brad thinks Cara's talents haven't been explored properly and he wants to take her under his wing," a source said.
"He's hoping she might sign an ongoing deal with his company."
Cara, 23, reportedly declined the "World War Z" sequel offer.
She "can't do it because of schedule conflicts."
Following her roles in "Paper Towns" and "Pan", Cara will next be seen in "Suicide Squad" and Luc Besson's "Valerian and the City of a Thousand Islands". Brad, meanwhile, will be seen in upcoming comedy war film "War Machine".
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