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President-elect Donald J. Trump is considering an executive order to allow TikTok to continue operating despite a pending legal ban until new owners are found, according to a person with knowledge of the matter.

The possible executive order, reported earlier by The Washington Post, is under discussion as TikTok faces a deadline on Sunday to be banned in the United States unless it finds a new owner. The popular video-sharing app is owned by ByteDance, a Chinese company. Republicans have said for years that they see the app, which has been downloaded to millions of smartphones, as a national security risk. It has become a rare issue that has united both parties in Congress.

If the Supreme Court upholds the law, which will ban the app unless ByteDance sells it to a non-Chinese company, special treatment from Mr. Trump might be the only way for TikTok to continue operating in the United States in the near term. The law requires app store operators like Apple and Google and cloud computing providers to stop distributing TikTok in the United States.

An executive order could try to direct the government not to enforce the law or to delay enforcement to complete a deal, a move that past presidents have used to challenge laws. It is unclear if an executive order would survive legal challenges or persuade the app stores and cloud computing companies to take steps that could expose them to huge penalties.

Alan Z. Rozenshtein, a former national security adviser to the Justice Department and a professor at the University of Minnesota Law School, said an executive order should be “taken with a medium-sized boulder of salt.” Such an order is not a law, he said, and legally would not change the legislation passed by Congress and signed by President Biden.

While there is some speculation that the app will still work if it has already been downloaded, the law also affects internet hosting companies like Oracle and other cloud computing providers, and it is unclear how video load times and the functionality of the app may respond.

One person close to Mr. Trump’s team said some of his allies had loose discussions about buying TikTok but provided no details. Mr. Biden, whose term ends on Monday, a day after the ban is set to go into effect, is also under pressure to find a way to save the app.

The New York Times reported late Wednesday that TikTok’s chief executive, Shou Chew, is expected to attend Mr. Trump’s inauguration on Monday and was offered a seat on the dais. TikTok declined to comment.

Mr. Chew is expected to be joined by other tech executives on the dais: Mark Zuckerberg, the co-founder of Meta; Jeff Bezos, the Amazon founder; Elon Musk, Mr. Trump’s megadonor; and Tim Cook, the chief executive of Apple, who personally donated $1 million to the inaugural committee.

Mr. Trump had previously backed a TikTok ban but publicly changed his stance last year, soon after meeting with Jeff Yass, a Republican megadonor who owns a large share of ByteDance.

Mr. Trump has said they did not discuss the company. But Mr. Yass helped found the trading firm Susquehanna International Group and is one of the biggest supporters of the conservative lobbying group Club for Growth. The group has hired people with ties to Mr. Trump, such as Kellyanne Conway, his former top adviser, and the Republican adviser David Urban, to lobby for TikTok in Washington.

TikTok has also worked to make inroads with the Trump team through Tony Sayegh, who was a Treasury official during Mr. Trump’s first administration and now leads public affairs for Susquehanna.

Mr. Sayegh has relationships with the Trump family and was a core part of the campaign’s decision to join TikTok this summer. Several members of the family, including Ivanka Trump, Donald Trump Jr. and Kai Trump, the president-elect’s granddaughter, have also joined the app.

Mr. Trump’s interest in TikTok is not entirely because of his advisers. He came to see how well videos about him performed on the platform, and his advisers credited it with helping him to expand his reach to a new type of voter during the campaign.

Any actions Mr. Trump might be able to take on TikTok are complicated. The law gives the president the ability to extend the deadline for a sale only if there is “significant progress” toward a deal that would put the company in the hands of a non-Chinese owner.

It also requires that the deal be possible to complete within 90 days of an extension. It is unclear exactly how an extension will work if Mr. Trump tries to deploy it after the ban takes effect.

TikTok has maintained throughout its court challenge to the law that such a sale is unworkable in part because of the prescribed time frame. A group led by the billionaire Frank McCourt has mounted a bid to buy the app — though without its mighty algorithm — in recent months.

Mr. Trump could also try to work around the law by instructing the government not to enforce it.

But app store operators and cloud computing providers could require more than a soft assurance from Mr. Trump that he will not punish them if they fail to execute the ban, said Ryan Calo, a professor at the University of Washington School of Law. The potential legal liability for companies that violate the law is significant: Penalties are as high as $5,000 per person who is able to use TikTok once the ban is in effect.

“You could have a policy not to enforce this ban,” said Mr. Calo, who was part of a group of professors who urged the Supreme Court to overturn the TikTok law. “But I think that maybe conservative companies would just be like: ‘OK, you’re not going to enforce it. But it is on the books, and you could enforce at any time.’”

Mr. Trump’s pick for attorney general, Pam Bondi, has declined to say whether she would enforce the law.

“I can’t discuss pending litigation,” she said at her Senate confirmation hearing on Wednesday. “But I will talk to all the career prosecutors who are handling the case.”

Mr. Trump has a third option: appealing to Congress to reverse a policy it overwhelmingly approved with broad bipartisan support last year.

“Congress can undo this anytime,” Mr. Calo said.