News reports in South Korea and the United States have mentioned Geneva and the Mongolian capital, Ulan Bator, as possible venues.

Mr. Moon has tried to be a mediator between Mr. Kim and Mr. Trump. His envoys met with the North Korean leader in Pyongyang in March, and went to Washington soon afterward to tell Mr. Trump that Mr. Kim wanted to talk.

According to South Korean officials and analysts, Mr. Moon hopes for a “comprehensive deal” in which Mr. Kim would commit to dismantling his nuclear arsenal and Mr. Trump would reciprocate by offering security guarantees for the North, including normalized ties with Washington.

But implementing such a deal would probably be extremely complicated and protracted. Past talks between North Korea and the United States have had similar aims, but they all collapsed in the early stages, over disputes about freezing the North’s nuclear activities and how such a freeze would be verified.

North Korea, as it has in the past, insists on a “phased” and “synchronized” implementation of any denuclearization deal. According to former South Korean officials who have dealt with the North, it fears that any deal it signs with Washington could come to an end after a change in American administrations. So rather than surrender its nuclear facilities up front, it wants incremental steps, matched with corresponding incentives from the United States.

For their part, American officials have said that North Korea has never been sincere in dealing with them, using negotiations to buy time while persisting in clandestine nuclear weapons development. Some hard-liners in Washington, like Mr. Trump’s new national security adviser, John R. Bolton, have demanded a quick dismantling of the North’s nuclear weapons program, suspecting that the North only wants to ease the tough international sanctions against it in exchange for a temporary, and deceptive, freezing of its nuclear program.

South Korea hopes that North Korea and the United States will agree on a road map toward denuclearization and quickly implement key steps before Mr. Trump’s term ends in January 2021, according to scholars advising Mr. Moon’s government. They said that a key challenge for Mr. Moon would be to persuade Mr. Kim and Mr. Trump to exchange key trust-building steps soon after they meet, like granting inspectors unfettered access to the North’s nuclear facilities and setting up liaison offices in each other’s capitals.