Kim made a surprise trip to the Chinese capital to meet Xi in late March and invited him to visit Pyongyang.
Moon is set to meet the reclusive North Korean leader next Friday for what would be a third inter-Korean summit.
Kim meanwhile, spent the weekend celebrating "The Day of the Sun", the birthday of his grandfather Kim Il Sung, by watching a performance by a Chinese ballet troupe along with wife Ri Sol-Ju.
It would be the first visit to North Korea by a Chinese president since Hu Jintao back in 2005.
But in late March, Kim made a visit to Beijing, his first known journey overseas since he took power in 2011. He will be the first North Korean leader to step on South Korean soil since the 1950s. Meeting Kim Jong-UN and Donald trump is expected to take place in may or June of this year.
It remains unclear at this time whether or not such an ambitious agenda can be achieved given the uncertainty of North Korean demands, which could potentially include the removal of strategic American military assets from South Korea, halting the deployment of nuclear or strategic assets during joint military exercises with South Korea, assurances that the US will not conduct a conventional or nuclear attack, the conversion of the armistice agreement into a peace treaty, and normalized diplomatic relations between Washington and Pyongyang.
In what would amount to a stunning development, North and South Korea are in discussions to announce at next week's leaders' summit an official end to the military conflict between the two neighbors, which remain technically at war, the South's Munhwa Ilbo daily reported Monday, citing an unidentified "key" South Korean official.
The two Koreas may also discuss pulling some of their forces away from the heavily fortified demilitarized zone separating them, the newspaper said.
North Korea has accused the United Kingdom of an "act of war" for deploying ships off the Korean peninsula, an action carried out by London to enforce worldwide sanctions against Pyongyang as a result of its nuclear and missile programs.