Southpaw will see Eminem play a welterweight boxing champion who recovers from a personal tragedy by succeeding in the ring.
Fuqua is currently in talks with DreamWorks, who is aiming for production to begin in the autumn, according to the Los Angeles Times.
The director, who is currently working on a biopic of drug lord Pablo Escobar, is also attached to an untitled biopic of dead rapper Tupac Shakur.
DreamWorks has prioritised Southpaw after the success of boxing drama The Fighter, says The Hollywood Reporter.
Southpaw could mark the return of Eminem in front of the camera, after his critically acclaimed turn in 2002's semi-autobiographical 8 Mile.
Eminem said last month that he was looking at several projects but wanted to find something "dope enough to put down the mic for a second".
Watch the original trailer for 8 Mile below: