Warner Bros is courting the actor-director and no official offer has been made nor has any commitment, according to The Hollywood Reporter.
Sources say that Gibson, 61, is familiarizing himself with the material. But the studio has not taken a call yet and is also looking at other directors, including Daniel Espinosa.
David Ayer wrote and helmed the first film, which featured an all-star cast that included Will Smith, Margot Robbie and Jared Leto.
The movie faced some initial hurdles during production and was met with somewhat polarizing response, but grossed USD 745 million worldwide.