BEIJING — Wu Xiaohui, the Chinese tycoon who was in failed talks with President Trump’s son-in-law, Jared Kushner, to buy into a skyscraper project in Manhattan, is fighting allegations of financial chicanery and has threatened to sue a Chinese magazine that examined his company’s labyrinthine funding.

The Anbang Insurance Group, which Mr. Wu controls as president and chief executive, said on Sunday that it would take legal action against Caixin Media and its editor in chief, Hu Shuli, after Caixin Weekly magazine questioned whether Anbang was as financially robust as the company claimed.

“Anbang’s shareholder structure is like a maze,” Caixin said in an article published online on Saturday and in print on Monday. It said that Anbang’s meteoric growth and acquisitions raised suspicions of financial sleight of hand, including capital injections coming from companies linked to Mr. Wu.

“The left hand has been helping the right hand to inflate capital,” the article said.

Anbang hit back with its own incendiary accusations. Caixin is a widely respected economics weekly, and its findings echoed an extensive report on Anbang by The New York Times last year. But Anbang suggested on Sunday that Caixin had published its report after failing to squeeze advertising orders and other contributions from Anbang.