The courtroom drama is being developed by and will star Robert, The Hollywood Reporter said.
Warner Bros is courting 75-year-old Jack in the hope that he will take up the role of a judge, who is Robert's character's father.
David Dobkin is attached to direct the movie, which will see Robert play an attorney who returns to his hometown for his mother's funeral to find that his estranged father, the town's judge, is the murder suspect.
Sources told The Hollywood Reporter that the Iron Man star, who is co-producing The Judge, is due to meet Jack later this week.
The Shining star Jack is said to be extremely picky about his film roles, and has made only three movies since 2003, The Departed, The Bucket List and most recently, How Do You Know in 2010, a romantic comedy co-starring Reese Witherspoon, Owen Wilson and Paul Rudd.