The recent South Korean summit and the potential USA talks have received more attention internationally, but China's role as an economic lifeline for North Korea makes the talks between Xi and Kim all the more crucial.
The leaders met in person for the first time during a secret meeting in the Chinese capital of Beijing in late March, which was widely viewed as a sign of warming ties between the two fractious allies.
According to state-run Korea Central News Agency (KCNA), Kim had seen two clocks on the wall that showed two separate times for the Koreas.
Trump said on Twitter that he will be speaking to Xi about later on Tuesday, adding that North Korea would be one of the topics they would talk about.
China's top diplomat, Wang Yi, met with Kim in Pyongyang last week, the first trip there by a Chinese foreign minister since 2007.
He was also quoted as saying: "I hope to build mutual trust with the USA through dialogue".
Kim Jong-un has ventured out of North Korea once again to meet another world leader.
Speculation had been swirling online earlier Tuesday of a mystery visitor to the northern Chinese province, including reports of a North Korean plane touching down.
A North Korea's Air Koryo plane lands in an airport in Dalian, China, Tuesday, May 8, 2018.
Chinese state media have quoted Mr Kim telling Mr Xi that his country remains committed to denuclearisation and has no need to possess nuclear weapons if a "relevant party" drops its "hostile policy and security threats" against it, in a clear reference to the United States.
"I do think North Korea would have a very strong interest to pivot to economic development", Zhao said.
He said that he is willing to work together with Kim to continue to guide relevant departments of the two sides to soundly implement the consensuses they have reached, promote the continuous advancement of China-DPRK relations, benefit the two countries and two peoples, and make positive contributions to the peace and stability of the region.
China is North Korea's most important economic and diplomatic backer, but Beijing has been angered by Pyongyang's repeated nuclear and missile tests and supported tough United Nations sanctions against its Cold War-era ally.
The South Korean government is exploring ways to increase economic cooperation with North Korea without breaching worldwide sanctions or earning the ire of Trump.
The Chinese foreign ministry would not confirm or deny that a North Korean official had visited the country.
For his part, Kim said both the DPRK-China friendship and the Korean Peninsula situation have undergone meaningful progress since March this year.
Dalian was also the site of a 2010 meeting between Mr. Kim's father, Kim Jong-il, and Mr. Li, who is now China's premier.
Hong Kong's South China Morning Post newspaper cited two unidentified sources as saying that Xi had flown to Dalian on the coast east of Beijing to meet with the official as well as to preside over the official launch of sea trials for China's first entirely self-built aircraft carrier. Others claimed to have spotted Red Flag limousines used by the statesmen, AP said.