"The US should give some sort of leverage to Seoul such as a more flexible operation of inter-Korean economic exchange and cooperation," the adviser said, as quoted by the Yonhap news agency.
Moon stressed it would be a "herculean task" for the South Korean leader to act as mediator, given that Pyongyang considered Seoul as Washington's ally.
The adviser expressed hope that President Moon would manage to agree with Trump on sanctions relief that could help to "reactivate" inter-Korean relations.
"I think President Moon's primary concern will be some kind of relaxation of sanctions from the U.S…. There could be some exemptions for inter-Korean exchanges perhaps, including Mount Kumgang and the Kaesong complex," he said.
North Korean leader Kim Jong-un and Moon agreed back in September 2018, amid a thaw in inter-Korean relations, to reopen the joint Kaesong industrial complex, which was closed in 2016 over Seoul-Pyongyang tensions, and also to relaunch the previously suspended tourist programs envisaging trips to North Korea's Mount Kumgang.
However, no specific steps have been made so far.
Trump and Kim held their second summit in Hanoi in late February in an attempt to give the denuclearization process more momentum.
The highly anticipated meeting failed to produce an accord. Negotiations fell apart after Pyongyang said it wanted Washington to lift all sanctions on the country before it started denuclearizing, while the United States could not agree.