News Corp chief Rupert Murdoch told his son James that he should go on leave as the phone hacking scandal unravelled this summer - but he changed his mind after a sleepless night, according to an article in Vanity Fair.
The article, in the magazine's December issue, says Rupert Murdoch's daughter Elisabeth pushed the suggestion.
It also claims the family has been undergoing psychological counselling over who will succeed the 80-year-old to run the media conglomerate.
The article comes as James Murdoch, News Corp's 38-year-old deputy chief operating officer, faces increasing pressure over his handling of the affair.
He will face a Commons committee for the second time on the issue next week.
News Corp declined to comment on the article.
The story's author, Sarah Ellison, is a former reporter for The Wall Street Journal, which is owned by News Corp.
Among other claims in the Vanity Fair article are that Rupert Murdoch has four votes in a family trust that controls nearly 40% of News Corp's voting stock, and his four eldest children, Prudence, Elisabeth, Lachlan and James, each have one.
That arrangement was reached in a divorce settlement with his second wife, Anna Torv, in 1999. The vote count is integral to understanding how disagreements between the siblings and their father might affect a possible power struggle when Rupert Murdoch steps down.
The article also claims that his young daughters Grace and Chloe by third wife Wendi Murdoch have no votes in the trust, but each, along with Wendi, were given a 150 million US dollars (£94 million) disbursement from the trust, which suggests they are not likely to play an active role in the company in the future.