Donald Trump has said his company will be run by his sons and won’t strike new foreign deals, but some he has already made present a challenge to his attempts to separate his presidency from his international business.

At the Wednesday press conference where Mr. Trump described the company’s new structure, he also said he had turned down $2 billion in property deals in Dubai to avoid any possible ethics issue. Dubai investor Hussain Sajwani confirmed he made those offers and that they were declined. But his company and the Trump Organization are still developing two golf courses in Dubai, one of which is set to open to the public by next month.

Mr. Sajwani is among several Asian and Middle Eastern partners of the Trump Organization who have faced government investigations or been sanctioned for corruption, stock fraud or tax evasion. Such troubles among business partners could prove tricky for a Trump administration’s relationship with those governments.

“The notion that there won’t be new deals doesn’t solve the problem of all the existing deals and businesses,” Walter Shaub, director of the U.S. Office of Government Ethics, said in a speech on Wednesday.

Problems among some of the Trump Organization’s partners include a tax probe in Indonesia, a conviction for stock manipulation in Malaysia, and Mr. Sajwani’s sentence—later overturned as Egypt’s political situation shifted—for an allegedly corrupt land deal there.