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.
Murdoch - whose News Corporation empire controls major outlets including Fox News and the Wall Street Journal in the US, and The Sun and The Times in the UK - was previously said to have been devoting more time to his new wife.
At the time of his marriage, the billionaire announced on Twitter that he was "the luckiest AND happiest man in world", and would stop posting on the platform.
In 2018, his elder son Lachlan was named as his successor. Murdoch also sold most of 21st Century Fox to the Walt Disney Company.
The couple had also been spotted together in public on several occasions.
Last year, Hall was seen "doting on" her partner at his 90th birthday party, according to the New York Times.
The Texan model-turned-actress was previously in a long-term relationship with Jagger, with whom she had four children. The pair tied the knot in a Hindu wedding ceremony in Bali, Indonesia, in 1990. The marriage was annulled less than a decade later in London's High Court of Justice.
Murdoch was previously married to Australian flight attendant Patricia Booker, from 1956 to 1967; Scottish-born journalist Anna Mann, from 1967 to 1999; and Chinese-born entrepreneur Wendi Deng, from 1999 to 2014.
Across their marriages, the pair have 10 children.