Donald Trump and Xi Jinping have a problem that's hard for them to discuss

China and the US have a big problem in common

When Chinese President Xi Jinping meets with U.S. President Donald Trump sometime soon, it would be in the interest of both politicians to find common ground on the threat posed by North Korea. But that's a lot more easily said than done.

"If it isn't primarily about North Korea, it's a mistake," said Derek Scissors, a scholar at the American Enterprise Institute and chief economist of the China Beige Book. In fact, the threat posed by the pariah state may be one of the few topics on which Beijing and Washington share common ground.

"The administration is not really prepared to engage China on a broad number of issues," Scissors said. The United States and China remain far apart on trade, currency issues, foreign investment and other economic topics.

Trump's White House has in recent weeks refrained from much of the tough talk it directed at China during the campaign and immediately after the election. Meanwhile, the administration has made North Korea a foreign-policy priority — new Defense Secretary Jim Mattis made his first overseas trip to South Korea.

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It's in the interest of both China and the United States to discuss North Korea: In the last few months, the dictatorship of Kim Jong Un has threatened U.S. allies and stepped up tests of missiles that could reach northeastern China. Kim's exiled half brother Kim Jong Nam — who is believed to have been under China's protection — was murdered in mid-February when he ventured into Malaysia.

"There will certainly be pressure from the Trump administration to deal with [missile tests] and rein it in," said Bruce Bennett, senior defense analyst at research organization Rand Corp. But China's response, he said, will likely be that "they really don't have much control on North Korea."

As the rogue state's largest trading partner, China has influence over North Korea. Beijing suspended coal imports from North Korea in February after Kim Jong Nam's murder and another missile test.

Shared problem, different goals

The two superpowers have a hard time discussing North Korea, however, because they have conflicting goals for the peninsula. Beijing wants to maintain the status quo, thereby avoiding a collapse of the north that could trigger refugee problems or a unified Korea that tilts toward the United States.

The U.S. administration, on the other hand, has said openly that it opposes maintaining the current situation, which has essentially given North Korea decades to continue advancing its missile technology and nuclear weapons.

"The policy of strategic patience has ended," Secretary of State Rex Tillerson said this month in South Korea. "We are exploring a new range of diplomatic, security, and economic measures. All options are on the table. North Korea must understand that the only path to a secure, economically-prosperous future is to abandon its development of nuclear weapons, ballistic missiles, and other weapons of mass destruction."

Also this year, China retaliated against U.S. ally South Korea for allowing the U.S. deployment of a missile defense system in the country. Beijing has impeded individual South Korean firms from doing business in China.

"The best outcome would be the U.S. and China have some clear and coherent policy" on how to deal with North Korea, said Charles Freeman, III, managing director at consulting firm Bower Group Asia and former assistant U.S. trade representative for China affairs.

"I don't know that that's possible or likely. I'm afraid we — China and the U.S. — are still at the stage of talking past each other on" North Korea, he said.

No date has been officially announced for the meeting between the leaders of the world's two biggest economies.

On Monday, the the Palm Beach Post reported that Police Chief Sean Scheller of Lantana, Florida, said that Xi is scheduled to visit from April 6 to 7. A senior state department official also confirmed the rough timing of Xi's visit in a press briefing Tuesday.

The White House did not immediately return CNBC's request for comment.