An attorney said the family will try to "get to the bottom" of the "internal decision-making process" leading to cancellation of the book, ABC News reported.
A November news release from publisher Harper Collins described the book as a "bone-chilling account" of the killings of Simpson's ex-wife Nicole Brown Simpson and Goldman, with Simpson picturing himself "at the center of the action."
Public outcry stopped publication of the book but Simpson told a Florida radio station he was paid for it and spent the money on bills.
Judith Regan, who handled the book for Harper Collins' Regan Publishing program, was fired because of the controversy. Regan had told The New York Times money for the book deal would go to Simpson's children via a third party.
Attorneys say Regan and Harper Collins and News Corp. executives could be deposed once the lawsuit is filed.