Donald J. Trump’s family business has an agreement to sell its marquee Washington hotel, reaching a deal to fetch at least $375 million for a property that prompted ethical scrutiny and struggled to make money even as it drew steady crowds of lobbyists, lawmakers and Trump loyalists.

The deal so far is what is known as a purchase and sale agreement, meaning a final sale of the Trump International Hotel has not taken place and may not happen until early next year, according to three people with knowledge of the matter.

The sale of the lease of the hotel, which operates out of a landmark federal building on Pennsylvania Avenue, comes after years of financial losses at the property, which opened in 2016, shortly before Mr. Trump was elected president.

Still, with the significant price of the planned sale, the Trump family is expected to turn a profit on the overall investment.

The buyer of the lease is CGI Merchant Group, a minority-owned real estate investment firm in Miami, according to the people briefed on details of the pending transaction, which was reported earlier by The Wall Street Journal.

CGI is exploring a deal to rename the hotel, based in the Old Post Office building, under the Waldorf Astoria luxury brand.

The sale must first be approved by the General Services Administration, the federal agency that controls the property.

From the time of its opening, the hotel immediately drew crowds of Trump supporters and favor-seekers. For a businessman president, it was the ideal bridge between his two worlds: a Trump hotel five blocks from the Trump White House.

This blurring between Mr. Trump’s business and his presidency fueled attacks from congressional Democrats who charged that he used the property as the hub of an influence-peddling operation.

Mr. Trump’s critics filed lawsuits against him, arguing that business that the hotel received from foreign governments violated the so-called emoluments clause of the Constitution, which prohibits federal officials from taking gifts or payments from other governments.

Mr. Trump’s company said that it voluntarily did not solicit business from foreign embassies, given the potential accusations of influence peddling. Mr. Trump also donated profits received from visits by foreign government officials, including those from Saudi Arabia, to the Treasury Department.

The controversies put a crimp in the hotel’s profits, people with knowledge of its finances have said, which worsened as the coronavirus pandemic dragged on, limiting travel and gatherings. Even as the hospitality industry has recovered, Mr. Trump’s departure from Washington sucked some of the energy out of the property.

But the hotel still served as a magnet for allies of Mr. Trump and top administration officials, who were often seen at the lobby bar, as well as Christian conservative groups and Republican congressional candidates who wanted Mr. Trump’s support.

The political operations run by Mr. Trump and his family, as well as the Republican National Committee, also spent hundreds of thousands of dollars at the hotel, as it became a frequent spot for fund-raising events. In total, more than $3 million in payments from political committees came in since early 2020 to the Washington hotel, Federal Election Commission records show.

The hotel, according to audits turned over to House investigators, still lost about $5 million to $10 million a year before depreciation losses were accounted for, meaning a total loss of about $74 million from 2016 to 2020, the audits showed.

But if the reported price for the purchase of the lease is completed as planned, it appears that the Trumps will gain a considerable profit on the sale, as the payment is higher than the capital investment the family made when renovating and opening the hotel. The sale of the lease allows the Trumps to pay off a loan they obtained for the property.

The company initially explored a sale of the property in 2019, but was unable to secure a deal before the pandemic.

CGI did not respond to a request for comment on Sunday. A spokeswoman for the Trump Organization did not respond to a request for comment.

The deal with CGI comes as Mr. Trump faces numerous costly and distracting criminal investigations, including by prosecutors in New York, who this year indicted the Trump Organization and its longtime chief financial officer, Allen H. Weisselberg.

The prosecutors are investigating whether Mr. Trump and his company artificially inflated his property values to obtain loans. Mr. Trump and his company have denied wrongdoing and called the investigation from the Manhattan district attorney, Cyrus R. Vance Jr., a Democrat, a politically motivated fishing expedition.

Citizens for Responsibility and Ethics in Washington, which sued Mr. Trump claiming that he violated the emoluments clause of the Constitution by accepting payments from foreign governments at the hotel, said the pending sale did not resolve the ethics issues associated with his ownership of the hotel while he was president.

“Selling it now that he’s out of office and the grift dried up is, to say the least, too little, too late,” said Noah Bookbinder, the president of the organization.

The lawsuit claiming constitutional violations by Mr. Trump in running the hotel while in office was ultimately dismissed after he lost his re-election bid and left the White House; the matter was then deemed moot by the Supreme Court.