The actress is considering the lead role in the untitled half-hour project, The Hollywood Reporter says.
The show, which is in the early stages of development, follows the ambitious headteacher of a prep school who notices the corruption in their city.
Davis stars in the new movie The Help and has previously appeared in television shows such as City of Angels, Law & Order: Special Victims Unit and United States of Tara. Her other film credits include Eat Pray Love, Doubt and Knight and Day.
Dee Rees, who recently wrote the movie Pariah, is said to be in talks to pen the HBO project. She would work alongside Margaret Nagle, whose credits include Boardwalk Empire and My So-Called Life.
HBO currently has a number of projects in development, including a drama about a reformed drug addict starring Julianne Moore.
Other shows in the works include baseball drama The Art of Fielding, Aaron Sorkin's broadcast newsroom drama More As This Story Develops and an adaptation of the novel Skinny Dip.