The two Koreas are technically still at war as the 1950-53 Korean conflict ended with a truce, not a peace treaty.
South Korean media reports that the two sides had been discussing plans for a permanent end to the war at the North-South summit, citing an unidentified Seoul official.
Kim is scheduled to make history when he meets President Moon at a summit just inside South Korean territory on April 27.
He will be the first North Korean leader to step on South Korean soil since the 1950s.
The two Koreas may also discuss pulling some of their forces away from the heavily fortified demilitarized zone separating them, the newspaper said.
Kim is also due to meet U.S. President Donald Trump in May or early June – if the U.S. leader is to be believed.
However, White House officials are still skeptical of the anti-American dictator’s sudden diplomatic efforts.
Last week, Secretary of State nominee CIA Director Mike Pompeo said North Korea should not expect rewards from talks until it takes irreversible steps to give up its nuclear weapons.
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.
Unlike previous years, the annual celebrations did not include the military parades displaying ballistic missiles often associated with the dictatorship, and the festivities had a reconciliatory overtone as shown by the invitation of a Chinese dance group.
Photos released by state media showed no weapons but instead a weekend of performances, fireworks, dancing and sports.
Kim and his wife were seen applauding, posing with dancers, and laughing with the head of the Chinese Communist Party’s international liaison department, Song Tao.
Kim, in a meeting with Song on Sunday, said he was personally meeting the visiting performers out of respect for Chinese President Xi Jinping and said he wanted to launch a ‘fresh phase of development’ of relations between their countries.
North Korea´s ties with China, its sole major ally, had become strained over the past couple of years over the North´s contentious missile and nuclear tests, which China disapproves of.
But in late March, Kim made a visit to Beijing, his first known journey abroad since he took power in 2011.