The summit between the two in June previous year was the first ever meeting between the leaders of the USA and North Korea.
Trump's comments Sunday seem to be a call for North Korea to return to a fresh round of high-level talks, said Shin Bum-cheol, a senior fellow at the Seoul-based Asan Institute for Policy Studies.
The train had been due to arrive in Beijing around 10 a.m. Tuesday.
The summit with Xi comes as Kim and President Donald Trump are negotiating over the location for a second summit meeting, and would also come on Kim's 35th birthday on Tuesday.
Shi Yinhong, an global relations professor at Renmin University in Beijing, said Kim's trip would have no direct influence on the progress of trade talks.
"If you come to South Korea, the day when our suffering colleagues and North Korean citizens are liberated from the fetters would be moved forward", he said in the letter released on his website. The despot made his first visit a year ago in March - which officials first confirmed days after a mystery train was spotted arriving and leaving a train station in the Chinese capital of Beijing.
The NIS reportedly said Jo had not made with South Korean agents, but Kim wouldn't say if the agency told lawmakers his current location or whether he intends to defect.
Kim said the NIS official said that Jo and his wife left the official residence in early November, weeks before his term was to end in late November.
"It will be announced probably in the not too distant future".
"They do want to meet and we want to meet and we'll see what happens".
The visit, reported today by Chinese state-run news agency Xinhua, is the fourth summit between the two leaders.
Trump and Kim met to discuss denuclearizing the Korean peninsula last June in Singapore, but little headway has occurred since then.
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An official with the Italian Foreign Ministry said the North Korean hadn't requested asylum from Italy.
"We have reported that the NIS cannot confirm the material and the exile status of the couple", Kim said, JoongAng Ilbo.
"Kim's confidence stems from the expectation of growing and reliable support by China", Rudiger Frank, a professor of East Asian economy and society at the University of Vienna, wrote on the North Korea-watching 38 North blog on January 2.
Chinese President Xi Jinping invited Kim Jong-un.