President Trump has gotten no love back yet from Kim Jong-un. He could turn to Xi Jinping, China’s leader, to help set up a summit when Mr. Xi visits Washington next week. For Mr. Trump, a summit with Mr. Kim would help him turn the spotlight away from the unpopular and costly war that he and Israel started against Iran and toward a leader-to-leader relationship that Mr. Trump has treasured since his first term.

The overtures from President Trump to one of his favorite dictators came hot and heavy over the summer. In June, Mr. Trump posted a photo of himself strolling through the tropical grounds of a luxury hotel with Kim Jong-un, the leader of North Korea, during their historic summit in Singapore eight years ago. Weeks later, he wrote online that the two had a “very good relationship.” In that post, Mr. Trump announced that the American military would dial back exercises with South Korea, shocking the close U.S. ally and handing Mr. Kim a gift. Three days later, when a reporter asked whether he would meet with Mr. Kim this year, the American president said, “Yeah, I will be.”

The courtship is on. The question in the coming weeks is whether it will be requited. Mr. Trump is expected to discuss North Korea with Xi Jinping, the leader of China, when Mr. Xi makes a state visit to Washington next week. China is North Korea’s oldest and most important ally. Mr. Xi is reluctant to have the United States and North Korea grow closer. But he could see helping broker a Trump-Kim summit as a favor to Mr. Trump and a way to gain leverage on other U.S.-China issues, a former Trump administration official said. It would also give Mr. Xi some control over the diplomacy.