The show will be directed by Noah Baumbach (Greenberg) and executive-produced by Baumbach and author Franzen together with film producer Scott Rudin.
Rudin, who has worked with Baumbach on several projects, had first optioned The Corrections in August 2001.
Baumbach and Franzen have co-written the adaptation of the award-winning 2001 novel, which explores the lives of an elderly couple and their three children.
Anthony Hopkins has expressed a desire to play the male lead in the show, Deadline reports, and has a meeting planned with producers.
Rudin is also currently developing another HBO pilot, More As This Story Develops, which has been penned by Aaron Sorkin.