The moves do not necessarily indicate that President Trump or the Trump Organization will eventually open a Trump hotel or casino there. But the ongoing efforts to expand Trump trademarks overseas have raised questions about whether they fall afoul of a constitutional prohibition on receiving economic benefits from foreign governments.
Since winning the presidential election, Mr. Trump has turned over control of his businesses to his adult sons, and his legal team has said the business would no longer pursue new foreign deals.
DTTM Operations, a New York company that holds Trump trademarks, applied in June for rights to the Trump name in casinos, construction, hotels and real estate, according to Macau government filings. It is not clear whether the applications were for new trademark protections or to renew similar trademarks dating back to 2006 that had expired.
The company already holds more than a dozen trademarks in Macau. Last year Trump won a legal battle with a Macau company that had registered to use the name "Trump" in coffee shops and restaurants.
A Trump Organization representative did not respond to a request for comment on Monday. The South China Morning Post reported on the filings on Sunday.
Macau, a former Portuguese enclave on China's southern coast that returned to Chinese control in 1999, is the only part of China where casino gambling is legal. After it opened up its gambling monopoly in 2001, new casinos and an influx of visitors from mainland China led to a full gambling boom, attracting American companies like Las Vegas Sands and Wynn Resorts. The tiny enclave surpassed the Las Vegas Strip for total revenues in 2006.
Mr. Trump began operating casinos in Atlantic City in the 1980s, eventually running four that held as much as about 30 percent of the city's gambling market in the 1990s. His casino companies sought bankruptcy protection multiple times, and he quit the board in 2009.
Trump trademark applications in Macau go back to 2006 and include "Trump," "Donald J. Trump," "Trump Tower," "Trump International Hotel and Tower" and "Chun Pou" — a Cantonese version of Mr. Trump's name.
The licenses issued after Macau opened up its gambling monopoly will soon begin to expire, which could open the market further.
"Gaming concessions for the six casino operators in Macau will expire between 2020 to 2022," Desmond Lam, an associate business professor at the University of Macau, said by email. "The industry is still somewhat unclear what will happen to these concessionaires after that. Recently, there have been some rumors that the Macau government may allow a seventh operator to enter this market."
The Trump business has picked up efforts to protect its name in mainland China as well. China approved a Trump trademark for the use of his name in construction services in February, shortly after he acknowledged he would maintain American policy toward Taiwan, a key issue for China's leaders. The president's critics said the episode showed how his company's overseas endeavors create a perception problem and expose him to potential conflicts.
The Trump business now holds at least 125 registered or provisionally approved trademarks in mainland China for a variety of services and products. Last month a trademark for the Trump name in relation to hotel restaurants was officially registered. Mr. Trump has no businesses in China, but the trademarks give some protection of his name in a country where knockoffs are commonplace.
The Trump Organization says those trademarks are registered with an affiliate and have nothing to do with Mr. Trump.
After denouncing China and its large trade gap with the United States during the presidential campaign, Mr. Trump eased off his criticism in hopes Beijing would be able to help curb North Korea's missile and nuclear weapons program.
But in recent weeks Mr. Trump has declared China's efforts to constrain Kim Jong-un, the North's leader, a failure, declaring last month on Twitter he was "very disappointed in China."