The Republican presidential nominee, Donald Trump, is taking aim at the nation’s largest and most powerful left-of-center newspaper, the New York Times, in an attack that may expose how the newspaper is being propped up financially by a Mexican billionaire.

“My lawyers want to sue the failing @nytimes so badly for irresponsible intent. I said no (for now), but they are watching. Really disgusting,” Mr. Trump tweeted on Saturday.

In another tweet, Mr. Trump said “The failing @nytimes has gone nuts that Crooked Hillary is doing so badly. They are willing to say anything, has become a laughingstock rag!”

If Mr. Trump wants advice on successfully suing media companies, he can consult Peter Thiel, the billionaire technology investor who backs his candidacy and who introduced Mr. Trump at the Republican National Convention. Mr. Thiel bankrolled the lawsuit that put the website Gawker out of business and that forced its founder, Nick Denton, into personal bankruptcy.

Mr. Trump’s focus on “irresponsible intent” suggests he has indeed been conferring with lawyers on the matter. It suggests Mr. Trump has at least passing familiarity with the libel standard that the 1964 case of New York Times Co. v. Sullivan established for public figures. The Times coverage need not merely be false and defamatory, it has to be published with “actual malice,” that is to say, in reckless disregard for the truth or with knowledge of the falsehood.

I can understand Mr. Trump’s frustration with the Times coverage. Every day brings a new breathless and hypocritical Times hit piece. The latest front-page story took Mr. Trump to task for extracting tax breaks for his New York City real estate projects. The Times article failed to mention or disclose that the New York Times Company received $29,857,491 in precisely the same kind of state and local tax breaks and subsidies for its own headquarters tower in New York City.

A Times article about Mr. Trump’s campaign chief executive, Stephen Bannon, who ran the Beitbart web site, referred to a Breitbart article as “a rare case of a publication publicly challenging its own reporter.” This from a newspaper, the Times, whose own editor had a few months earlier issued a public statement denouncing an article the Times published as “clumsy” and “flawed” and accusing his own reporter of treating a colleague “unfairly.”

Then there is the Times suggestion that Mr. Trump’s Russian connections — “He staged a Miss Universe pageant in Moscow, explored real estate deals there and sold a Florida mansion to a Russian billionaire” — have somehow influenced his foreign policy. This is reported without any disclosure of the Times’s own Mexican connection.

For that, you have to go to the newspaper’s proxy statement, which discloses that, as of March 7, 2016, Carlos Slim Helu, of Mexico, controlled 17.4% of New York Times company stock, or 27,803,000 shares. At today’s prices, that’s worth about $344 million. For comparison’s stake, the entire Ochs-Sulzberger family, including the newspaper’s publisher, Arthur Ochs Sulzberger Jr., and all the trusts he and his cousins control, own a stake amounting to a mere 11%, according to the proxy statement. It’s a complicated situation, because there are two classes of stock and the class of shares controlled by the Ochs-Sulzberger family has control of the newspaper.

Meanwhile, the peso is plummeting against the dollar in a movement that closely tracks the polling gains of Mr. Trump. Imagine that Mr. Trump were to get elected, force Mexico to pay for a border wall, and abrogate or renegotiate the North American Free Trade Agreement in a way that is unfavorable to Mexico. And imagine that Carlos Slim suddenly needed to liquidate that $344 million New York Times investment.

Would there be other buyers out there willing to do what Mr. Slim has done, which is to put in more money than the Ochs-Sulzbergers without getting management control (and while leaving the family members with jobs at the company paying a total of more than $7 million in 2015)? If not, would the family choose to sell, as virtually every other longtime newspaper-owning family — from the Chandlers of the Los Angeles Times, to the Grahams of the Washington Post, to the Bancrofts of the Wall Street Journal — has done in recent years?

It’d be almost worth the legal fees for Mr. Trump (or Mr. Thiel’s anti-Gawker lawyers, working on Mr. Trump’s behalf) to sue the New York Times just to get discovery of the communications between Carlos Slim and Times Company executives regarding Mr. Trump and his chances of victory. Maybe there are no such communications, or maybe the Times has already gotten rid of them the same way that Hillary Clinton did with her emails. But if any such conversations do exist, they’d likely be of interest not only to Mr. Trump and his lawyers but to Times readers and the voting public.

Mr. Stoll is editor of FutureOfCapitalism.com.