For years, Beijing bristled at Washington’s demands that TikTok be sold off, dismissing the push as “robbers’ logic.” The video app, wildly popular with young Americans, became another front in the larger battle over technology, influence, and national security.

Now, China is signaling something different. Officials have begun floating the possibility that ByteDance, TikTok’s parent company, could part with its U.S. operations — a shift that has stirred speculation about what Beijing hopes to gain in return.

TikTok’s value lies not just in its audience of more than 170 million Americans, but in its algorithm — the recommendation engine credited …