Kim is seeking relief from economic sanctions in return for his pledge to denuclearise and is believed to be seeking support from China for that, the Nikkei said in a dispatch from Beijing.
Mr Kim's current visit to Beijing is his third to China within three months.
North Korean state media said in a report the day after the June 12 summit that Trump had agreed to lift sanctions - a claim that contradicted comments from the president that the measures would "come off when we are sure that the nukes are no longer a factor".
Ministry spokesman Noh Kyu-duk said Seoul and Beijing share a "strategic goal" in achieving the "complete denuclearization" of the Korean Peninsula and that progress in nuclear diplomacy has been facilitating high-level contacts between North Korea and its neighbors.
Kim Jong-un's latest trip to China has also sparked speculations that sanctions imposed by Beijing may be discussed.
"This is the Chinese way", said Hwang Jae-ho, a China expert at Seoul's Hankuk University of Foreign Studies, who was also traveling to China for meetings with his Chinese counterparts on the same day.
While Washington has said repeatedly it wants Pyongyang to commit to the comprehensive, verified and irreversible disarmament of the peninsula, the joint declaration signed at the Trump-Kim summit did not include any timelines or specific targets.
During his press conference in Singapore after the summit, Trump suggested he succeeded where past administrations had failed.
Xi said he was pleased to see North Korea's decision to promote economic reforms, adding that China's own reform and opening up process had meant the Chinese people's eyes had been open to the world.
He has been expected to visit the country to brief Chinese President Xi Jinping on his meeting with the U.S. president. Previous visits by North Korean leaders have been shrouded in secrecy and confirmed only after their departure.
The visit shows that China is "key" to the talks, Wang said.
In addition to discussing last week's Singapore summit, Kim is expected to ask China for help in easing economic sanctions in return for his pledge to denuclearize, according to Wang Dong, an global relations expert at Peking University.
Mr. Pompeo has defended the Singapore joint statement, in which Mr. Kim did express "unwavering commitment to complete denuclearization of the Korean Peninsula".
It was the first-ever summit between a sitting USA president and a North Korean leader.
Meanwhile, the US and South Korea have confirmed they have suspended planning for their next joint military drills.
"Although Kim was successful in solidifying his legitimacy to rule, he may not be totally happy with the result as there was no mention of easing the sanctions", he said, adding that Trump had not given up anything at a "practical level".