Although both men parlayed their inheritances into global power, they have stubbornly viewed themselves as outsiders at odds with the establishment. When Mr. Murdoch entered the British newspaper market in 1968, London society shunned him and his vulgar tabloids, The Sun and The News of the World, which he used to wound his enemies and advance his political interests. Mr. Trump withstood a similar wariness among the elite after he made himself a Manhattan player through his brazen deal making and hucksterism.

To make their way upward in New York, both men relied on a powerful friend, the lawyer Roy M. Cohn, a ruthless fixer who made his name in the 1950s as the chief counsel to Joseph McCarthy, the Red-baiting senator, before representing some of the city’s most powerful figures, including the mobster John Gotti and the New York Yankees owner George Steinbrenner.

Mr. Cohn connected Mr. Trump to Mr. Murdoch and the tabloid he bought in 1976, The New York Post. The upstart developer saw that he could benefit from the brash daily — especially its Page Six gossip column, which started a year after Mr. Murdoch became the paper’s owner.

“Trump was interested in specifically Rupert’s ownership of The Post, because Page Six is very important to his rising stature in New York City and branding efforts,” said Roger J. Stone Jr., a Republican operative who has known both men for decades.

Mr. Trump seemed to revel in the tabloid’s saucy coverage of his personal life. In 1989 and 1990, The Post turned out a series of front pages on Mr. Trump’s split from his first wife, Ivana Trump, and his affair with Marla Maples. The stream of headlines in bold block letters culminated in a quote attributed to Ms. Maples: “Best Sex I’ve Ever Had.”

Mr. Trump’s enthusiastic response to the planned Disney-Fox megadeal may have been lost in the swirl of Washington news had it not been for his vehement opposition to another recent attempt at media consolidation — AT&T’s proposed $85.4 billion acquisition of Time Warner, the parent company of CNN, a frequent target of the president’s “fake news” complaints. While so far making no move on the Disney-Fox plan, the Justice Department has sued to block the AT&T-Time Warner deal on antitrust grounds in a rare instance of governmental interference in a merger of two companies that do not directly compete with each other.