TikTok is one of the most popular and largest social media apps around the globe — with great brand recognition and loyal users.

It may also be one of the hardest to sell.

That’s the conundrum facing TikTok as Washington lawmakers push a bill that would force the app’s Chinese parent company, ByteDance, to sell it or face having it banned in the United States. The bill passed the House on Wednesday but could face an uphill climb in the Senate.

Rumors are already swirling on Wall Street about who could be interested in buying TikTok. The rumblings grew louder on Thursday after Steven Mnuchin, a former Treasury secretary, told CNBC that he was “trying to put together a group to buy TikTok, because they should be owned by U.S. businesses.” Mr. Mnuchin said he had spoken to a “combination of U.S. investors” about such a deal.

But any potential buyer could confront several roadblocks. The Chinese government could block the sale. The U.S. president, according to the bill passed by the House, would have to affirm that a deal cut the app off from ByteDance.

And then there is the price tag — almost certainly a large one. The research firm CB Insights recently estimated that ByteDance was worth $225 billion, though it is less clear how much the U.S. version of TikTok would cost on its own.

The price would limit the pool of potential buyers to a coalition of private equity firms; a corporate behemoth, like Microsoft; or a combination of the two. But it is unclear if antitrust regulators would allow a large company like Microsoft — or Alphabet, which owns YouTube — to buy the app.