“The concern I have is I’m not sure the North Koreans believe that. I think what they think is that by getting the U.S. out, they have a chance of unifying the Korean peninsula on their terms,” he said, adding if U.S. and South Korea were to cease their military exercises, it wouldn’t alleviate the threat from the North.

On Sunday, the White House said President Donald Trump spoke with leaders of China and Japan on several issues, including the threat from Pyongyang. Trump is reportedly becoming more frustrated with China’s inability — or lack of desire — to rein in North Korea. But Hill said the Trump administration needed to do much serious work with Beijing in order to tackle the threat — until now, the efforts have been episodic and making phone calls, according to Hill.

“I think the problem the Trump administration has had with China is they look at China as a sort of outsourcing place, where they can kind of turn it over to China and tell the Chinese, you figure it out,” he said.

Hill added that within China, people are likely divided over Beijing’s stance toward Pyongyang. Some worry that North Korea’s demise could be perceived by the Chinese public as a victory for the United States and defeat for China.

If the U.S. and China are seen cooperating in an attempt to stop North Korea’s nuclear ambitions, Hill said it is likely that Kim Jong-un will pay attention.

If Kim “gets the message that the U.S. and China are really cooperating at that level, he might have a second look at this,” he said.

— CNBC’s Leslie Shaffer contributed to this report.