In his memoir Making Headlines, Chris Mitchell, the former editor of the Australian, has claimed Mr Murdoch’s domestic staff reported this "closeness" to him.
He said Mr Murdoch, 85, was “clearly lonely and struggling to sleep” after separating from Ms Deng, 47, according to The Guardian. Mr Murdoch filed for divorce in November 2013 after 14 years of marriage. They have two children together and Mr Blair is godfather to one of their daughters.
In his memoir, Mr Mitchell writes: “It was clear that my boss had been devastated by the closeness he found between his wife and his former friend. I never asked what that was, but it is clear that his Australian family, alerted by domestic staff, rang the bell on whatever was going on when Rupert was out of town.”
Mr Blair, 63, has always strenuously denied having an affair with Ms Deng and there is nothing to suggest that he did.
He was a notable absentee from the guest list when Mr Murdoch married Jerry Hall in March this year.
Mr Mitchell said Mr Murdoch is now happy and settled after marrying the former supermodel.
“Oh, s**t, oh, s**t. Whatever why I’m so so missing Tony. Because he is so so charming and his clothes are so good,” the note reportedly read. Murdoch and Deng issued a joint statement in response in which they said they had made the decision “not to engage in public allegations or respond to negative claims”.
In December 2014, Mr Blair reacted angrily when he was asked about the issue during an interview with The Economist.
He is reported to have banged his coffee cup so hard that it made everyone in the room jump before going on to insist that the nature of his closeness with Ms Deng was “not something I will ever talk about. I haven’t and I won’t”.
Mr Mitchell, who became the editor of the Australian in 1992 and retired in 2015, described Mr Murdoch as a “loving patriarch and husband” and criticised the “caricature” he claimed left-wing media has developed of him.
Ms Deng, Mr Blair and Mr Murdoch did not immediately respond to a request for comment.
By Heather Saul