The Qatar Investment Authority bought a $1.8 billion stake in Brookfield Property Partners in 2014, and is the second-largest investor in the company, ranking only behind Brookfield Asset Management. And the Qatar fund and Brookfield have teamed up on several real estate deals in the United States and elsewhere in recent years, including Brookfield’s retail and apartment complex, Manhattan West, now under construction on Manhattan’s West Side. Brookfield and Qatar also control the Canary Wharf office complex in London.

The Qatar Investment Authority is one of the world’s largest sovereign funds, with $320 billion in assets under management, according to the Sovereign Wealth Fund Institute. In 2015 the fund announced plans to invest $35 billion in the United States, and it has since become a sizable commercial real estate investor, taking part in roughly $7 billion in real estate deals and buying up properties around New York and Los Angeles, according to CoStar Group, a real estate research firm.

Charles and Jared Kushner bought the tower at 666 Fifth Avenue in 2007, when, with a partner, they borrowed $1.75 billion for the purchase. The tower served as the price of admission to elite Manhattan real estate circles for a developer previously known for building and operating suburban garden apartment complexes in New Jersey and Pennsylvania.

But if the father and son team believed that they had purchased a real estate trophy in one of the most desirable locations in the city, the debt-laden tower turned out to be more of an albatross.

At the time they bought it, the building only generated enough cash to pay two-thirds of their annual debt payments. But they were betting on a quick turnaround and a big jump in rents.

The Kushners sold 666 Fifth Avenue’s prime asset — its Fifth Avenue retail space — for $525 million. But office rents fell during the recession, and two of the building’s biggest tenants left. In 2012 the Kushners were forced to restructure their loans, and Vornado Realty Trust bought 49.5 percent of the building’s office space and gave the Kushners an $80 million high-interest loan. Vornado later bought the Fifth Avenue retail space for $707 million.

In late 2016, Charles Kushner and his son were close to a much different kind of deal with Anbang, a giant Chinese insurance company with ties to the country’s ruling elite, and Mr. Al-Thani. That plan involved demolishing the existing building at 666 Fifth Avenue and erecting a $7.5 billion luxury super tower. But the deal collapsed a year ago, amid criticism from legislators over the connection between Jared Kushner’s political role and the family business.