President Jae-in is expected to travel to Pyongyang, North Korea’s capital, later this week, marking the first time a South Korean leader has done so in 11 years.
The visit is projected to last three days.
The South Korean leader is hoping to kick-start denuclearisation talks, which have stalled in recent weeks.
Moon Chung-in, a key aide to Mr Jae-in, said: “President Moon will try to persuade Kim to come up with some bold moves.”
He added that trust between North Korea and the US could be built if Kim Jong-un “comes up with some shocking concessions, and then the US responds boldly”.
In return he suggested: “America should provide North Korea with political assurances, a liaison office, military assurances, a non-aggression treaty and economic assurances with investments.”
Last month President Trump cancelled a planned visit to North Korea by Mike Pompeo, his Secretary of State, claiming the country has made insufficient moves towards denuclearisation.
Trump met Kim Jong-un in Singapore in June, becoming the first sitting US President to meet a North Korean leader.
However, limited progress has been made since the landmark summit.
The US is demanding North Korea abandons its nuclear programme before sanctions relief is granted, while the North Koreans are demanding continuous concessions.
Recent satellite images suggest North Korea has continued to work on its only known nuclear site.
North and South Korea, who technically remain at war, have opened a joint liaison office in Kaesong, just over the North Korean border.
Each side will staff the facility with 20 officials, establishing long-term communications.
Baik Tae-hyun, a spokesman for South Korea’s unification ministry, said: “We hope that this will also help the progress of denuclearisation talks between North Korea and the United States.”
President Jae-in and Kim Jong-un met for the first time in the border village of Panmunjom on April 27.
A month later, on May 26, they held a follow-up meeting at the same location.