LOS ANGELES (Reuters) - Arnold Schwarzenegger says his estranged wife has not read his upcoming memoir in which he discusses the secret child he fathered with a family housekeeper.

But in a TV interview with CBS program "60 Minutes," the action star turned politician said he was determined to write a book that included what he called his "failures" as well as his successful and multi-faceted career.

Schwarzenegger's book "Total Recall: My Unbelievably True Life Story," is to be published on October 1.

Publisher Simon & Schuster has said the former California governor began writing it before the May 2011 scandal over the son he fathered years earlier with his housekeeper while married to Maria Shriver.

The revelations led the couple to start divorce proceedings ending their 25-year marriage, and brought media ridicule for the "Terminator" star.

In an interview with "60 Minutes," to be broadcast in full on September 30, journalist Lesley Stahl asked Schwarzenegger, 65, if Shriver knew he was writing about the affair in his book.

"I think that Maria is, you know, wishing me well with everything that I do," he replied, in an excerpt shown on Monday on breakfast show "CBS This Morning."

While admitting that Shriver had not read the memoir, Schwarzenegger continued, "She knows that it's about my whole life and that I would not write a book and kind of leave out that part and make people feel like, 'Well, wait a minute. Are we just getting a book about his success stories and not talk about his failures?' And that's not the book I wanted to write. I wanted to write about the book about me. Here's my life."

According to an advance copy obtained by the New York Daily News, Schwarzenegger writes that he and housekeeper Mildred Baena had sex in 1996 in a guest house at the mansion he shared with Shriver while she and their children were away on vacation.

He was finally forced to admit he was the father of Baena's son in a couples counseling session with Shriver the day after he ended his term as California's governor in January 2011.

The Austrian-born former body-builder, who became one of Hollywood's biggest movie stars, is promoting the book on his official website with a video and the tagline, "This story you know. Are you ready for the story you don't?"

Since ending his term as Republican governor, Schwarzenegger has returned to movies with "The Expendables 2" in August and has five more films in the pipeline. He has also inaugurated a global policy think tank in his name at the University of Southern California at its Los Angeles campus.