President Trump’s real-estate business is considering unloading its opulent Washington, D.C., hotel, a move it says is motivated partly by criticism that the Trumps are flouting government-ethics laws by profiting from the property.

The family business, the Trump Organization, has hired the real-estate firm JLL to market rights to the Trump International Hotel, Eric Trump, an executive vice president of the company, told The Wall Street Journal. The Trumps don’t actually own the hotel, which is the former Old Post Office,...