The US president has never spoken in public about Mr Murdoch, 91, according to a database of Mr Biden’s speeches and other public statements.
But the president reportedly told an associate last year that he had “assessed” Mr Murdoch to be “one of the most destructive forces in the United States”.
The exchange was recounted in This Will Not Pass: Trump, Biden and the Battle for America’s Future, written by two New York Times reporters.
Mr Biden has publicly berated Fox News reporters, and made reference to the right-wing network’s critical coverage of his presidency.
Most recently, he was caught on a mic calling Fox’s White House reporter Peter Doocy a “stupid son of a b—-” in response to a question.
He later called Mr Doocy to apologise.
Mr Biden has also joked about the network’s negative coverage of his presidency, saying that he sometimes “turn[s] on Fox to find out how popular I am”.
Mr Biden’s aides have also hit back at Fox News’ coverage of coronavirus and its punditry on Vladimir Putin and Russia, claiming the network spreads misinformation.The president reportedly told an associate last year that he had ‘assessed’ Mr Murdoch to be ‘one of the most destructive forces in the United States’
The network is facing a $2.7 billion lawsuit over its coverage of Donald Trump’s claims that the 2020 election was rigged against him.
However, Fox News was the first major network to call the state of Arizona for Joe Biden, which essentially projected Mr Trump had no route to winning the 2020 election.
Mr Trump was furious at the decision, which was reportedly personally approved by Mr Murdoch. Fox has denied the claim.
Mr Murdoch has publicly called on Mr Trump to move on from the 2020 result, which the Republican continues to insist was a fraudulent election.
In a meeting with shareholders last year, the media tycoon said: “The past is the past, and the country is now in a contest to define the future.”
This Will Not Pass is published in May. Previous extracts from the book detailed reported tensions between Mr Biden and his vice president, Kamala Harris, describing their relationship as “friendly but not close”.
It also claimed the First Lady, Jill Biden, was opposed to Ms Harris becoming her husband’s running mate after she denounced him in a Democratic debate.
Ms Biden is said to have asked her husband’s aides: “There are millions of people in the United States… [why] do we have to choose the one who attacked Joe?”