North Korea will "make efforts for the second summit between (North Korean) and US leaders to achieve results that will be welcomed by the worldwide community", Kim was quoted as saying by China's official Xinhua News Agency.
The report came as Kim returned to Pyongyang after a trip to China, where he held talks with Xi and visited an economic development area in Beijing.
Trump and Kim reached an agreement to work toward the "complete denuclearization of the Korean Peninsula", during their first meeting in June in Singapore.
Progress between Washington and Pyongyang has always been hobbled by wide differences on how denuclearisation should unfold, and under what conditions.
He said North Korea needed to take "bold steps" towards denuclearisation in order to draw US concessions such as sanctions relief. The North Korean leader said in his New Year's address that he might take a "new path" in negotiations if Trump didn't ease trade, travel and investment restrictions.
He "spoke highly of the positive measures taken by the DPRK side", it added.
North Korea has repeatedly invited Xi to visit Pyongyang. "If he wants to shift his focus to the development of the economy, he needs China's cooperation", said Mr Lu Chao, a North Korea expert at China's Liaoning Academy of Social Sciences. His visit is also seen as part of an effort to win Chinese support for a reduction of United Nations sanctions imposed over his nuclear weapons and ballistic missile programs that have severely impacted his country's already ailing economy.
Kim spoke with Xi for about an hour Tuesday night, discussing ways to strengthen their ties and lay out strategy for a potential summit between Kim and Trump on curbing Pyongyang's nuclear ambitions, Yonhap reported, citing unidentified people familiar with the talks.
Despite starting his Presidency with explosive rhetoric against Kim, Trump has changed his tone considerably, and even went so far as to say "we fell in love" in September previous year. "Judging from the delegation lineup, the mission appears to place emphasis on North Korea's continuing diplomatic outreach and nuclear and security issues", Aoki said.More news: Timberwolves fire coach Tom Thibodeau
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"[China also] supports the DPRK and the United States holding summits and achieving results, and supports relevant parties resolving their respective legitimate concerns through dialogue".
Trump said Sunday that the United States and North Korea were negotiating the location of their next summit.
The visit coincides with what South Korean officials say is Kim's 35th birthday on Tuesday.
Kim could not be seen but the limousine he uses was observed zipping east down a main thoroughfare in Beijing on Wednesday.
Mr Kim made what is believe to be his first official trip outside North Korea to China a year ago, even before meeting South Korea's President Moon and Mr Trump.
Yonhap said Kim met with Xi for about an hour Tuesday and later attended a dinner at the Great Hall of the People in central Beijing hosted by Xi and his wife, Peng Liyuan.
Kim visited a pharmaceutical plant that makes traditional Chinese medicine on Wednesday and met Xi again for lunch at a hotel before heading back to North Korea by train.