Potential conflicts of interest for Mr. Trump as president have been documented around the world, including in Scotland, India, Brazil, the Philippines, Argentina and Turkey. But perhaps nowhere are the stakes quite as high as in Taiwan, because it involves ties between the United States and China, the countries with the world’s biggest economies and most powerful militaries.

“Even if the phone call had not happened, once these business dealings came to light, it would send a very confusing signal to Beijing,” said Marc Lanteigne, a senior research fellow at the Norwegian Institute of International Affairs who focuses on Chinese security issues.

Any business ties could undermine the near certainty that world leaders have had for many decades about some of the basic foundations of United States foreign policy, which has included the primacy of maintaining ties with China in a “very narrow framework,” said Shelley Rigger, a professor of political science at Davidson College in North Carolina who studies Taiwan-United States relations.

“It is very worrisome not just for leaders in China but for leaders everywhere to think that there could be motivations driving U.S. foreign policy that they can’t, A, know about and, B, work out logically,” Professor Rigger said by telephone. “If the U.S. government is being influenced by some kind of parallel set of side deals and interests that are not the sort of mainstream U.S. foreign policy and national interest agenda, then no one is going to be able to predict anything.”

Adding to the complexity is the fact that the Taoyuan Aerotropolis is a government-run development project, and Ms. Tsai’s administration must give final approval for the complex plan, which involves removing many people from their homes, before construction can begin. Taoyuan is the center of a metropolitan area with over two million residents.

Ms. Chen — who, according to online biographies of her, was raised in Las Vegas — has been associated with the Trump Organization for several years, and with Ms. Lu, the former vice president, for much longer. In December 2012, a photograph of the two women was posted on the Facebook page of the condominium sales arm of Trump International Realty in Las Vegas, thanking them for visiting. Ms. Chen also accompanied Ms. Lu, who was then the vice president, during a trip to Las Vegas in 2004.

“The Trump Organization said: ‘Hey, Ms. Chen, your business and politics connections seem great. Do you want to help us promote our Las Vegas properties?’” Ms. Chen said in an interview with a Taiwanese television station in late October.