China’s president, Xi Jinping, has never met Mr. Kim. Mr. Kim has not visited China since he became North Korea’s leader in 2011, despite a partnership between the two Communist neighbors.

If Mr. Kim was on the train, it would be his first trip outside his country as North Korea’s leader. He has never met any foreign head of state. If he meets Mr. Xi before his planned meetings with Mr. Trump and Mr. Moon, it could help mend the recently frayed ties between the two old Communist allies.

Mr. Kim’s aggressive drive for a nuclear arsenal able to strike the continental United States has drawn increasingly harsh criticism from Beijing, which has backed several rounds of increasingly stringent sanctions against North Korea. North Korean exports of coal, seafood and other valuable sources of currency have been reduced by the sanctions.

No official activity by Mr. Kim has been reported by North Korea’s state-run media since he met the South Korean envoys on March 5, when the two sides agreed to a meeting between Mr. Kim and Mr. Moon in the border village of Panmunjom in late April.

The South Korean envoys then visited the White House on March 9, delivering what they said was Mr. Kim’s offer to discuss denuclearizing his country with President Trump. Mr. Trump accepted the invitation on the spot and said he would meet Mr. Kim by May.

During this swirl of abrupt turns, China has mostly been a bystander, playing no direct role in the diplomacy. The Chinese Ministry of Foreign Affairs has said it welcomes the easing of tensions. But experts have said that Beijing would want to make sure that any negotiations protect its interests.

North Korea depends heavily on China for trade, food, energy and a degree of protection from even tougher international sanctions. But the North has bristled at the idea that it is beholden to China. And Chinese officials and many experts say that China’s influence over North Korea is more limited and brittle than Mr. Trump and other Western leaders seem to believe.

From 2003, Beijing hosted six-party talks which brought together North and South Korea, the United States, Japan, Russia and China to seek an agreement on ending the North’s nuclear program. But the talks foundered after 2009. More recently, Beijing has proposed that North Korea suspend its nuclear and missile tests in return for the United States and South Korea suspending major joint military exercises.