The 91-year-old Murdoch controls News Corp and Fox Corp through a Reno, Nevada-based family trust that holds roughly a 40% stake in voting shares of each company.
Bryce Tom, a spokesperson for Murdoch, declined to comment. A representative for Hall, who is 65, did not immediately respond to a request for comment.
The billionaire, whose net worth Forbes estimates at $17.7 billion, built a sprawling media empire with assets around the globe. He sold the Fox film and television studios and other entertainment assets to Walt Disney Co in a $71.3 billion deal that closed in March 2019.
Murdoch previously was married to entrepreneur Wendi Deng, whom he divorced in 2014 after 14 years of marriage. They have two daughters. He split from his second wife, Anna Murdoch Mann, a Scottish journalist with whom he had three children, in 1999. He and his first wife, Patricia Booker, a former flight attendant with whom he had a daughter, divorced in 1966.