The divorce would be a fourth for Murdoch, who is 91. Hall, 65, was previously married to Rolling Stones frontman Mick Jagger.
Representatives for Murdoch and Hall, who wed at a mansion in central London in 2016, are yet to comment.
Their split comes as a surprise to those close to the family, according to the New York Times.
That newspaper and the Washington Post cited anonymous sources with knowledge of the separation.