They say the Chinese leaders, who are unused to being on the outside looking in, are growing anxious about whether they can keep their Cold War-era ally firmly in its current orbit around China. Leaders in Beijing are worried, experts say, that Mr. Kim might try to counterbalance China’s influence by embracing the United States, North Korea’s longtime enemy.

According to analysts, Mr. Kim may seek to do this by offering Mr. Trump some sort of deal, which would probably include some pledge to scrap his nuclear arsenal in exchange for American help to reduce or even eliminate North Korea’s near total dependence on China.

“If you look at history, North Korea is not sure of China, and has a kind of revenge mentality,” said Shen Zhihua, a prominent Chinese historian on North Korea. “The worst outcome is that the United States, South Korea and North Korea all get together and China gets knocked out.”