Moon told reporters that Kim said he's willing to co-operate to end confrontation and work toward peace for the sake of the successful summit with Trump.
The United States and South Korea blacklisted him for supporting the North's nuclear and missile programs in 2010 and 2016, respectively, so a visit to the United States would indicate a waiver was granted.
The Trump administration is believed to have granted him a temporary waiver this time to allow him to NY, where North Korea has a diplomatic mission to the United Nations.
"Vice Chairman Kim bought a ticket for a flight to NY to depart at 1 p.m. today", a source said.
Mr Trump confirmed that Mr Kim Yong Chol is headed for NY.
But it was not immediately known what else he would do in the United States.
Despite repeated references to "denuclearization of the Korean Peninsula" by the North, it remains unclear whether Kim will ever agree to fully abandon his nuclear arsenal.
Speaking over the phone earlier in the day, the two leaders reportedly discussed "recent developments in North Korea" and agreed to "continue close coordination" through another face-to-face meeting in the days leading up to the planned summit.
Ivanka Trump was seated in front of Kim Yong Chol, vice-chairman of North Korea's ruling Workers' Party Central Committee, during the Winter Olympics closing ceremony.
White House Press Secretary Sarah Sanders also announced that President Donald Trump will host a meeting with Japan's Prime Minister Shinzo Abe June 7, a week before the Singapore summit. Since then, he has suggested the summit could be back on, and Kim Yong Chol's trip to the USA seems to imply that preparations for a meeting could be in the final stages.
While maintaining that Kim is committed to denuclearization, Moon acknowledged Pyongyang and Washington may have differing expectations of what that means and he urged both sides to hold working-level talks to resolve their differences.
A top North Korean official headed to NY on Wednesday for talks aimed at salvaging a summit between Kim Jong-un and President Donald Trump on the future of Kim's nuclear programme, in the North's highest-level mission to the United States in 18 years.
Moon has been scrambling to salvage a 12 June summit between Trump and Kim in Singapore after Trump abruptly cancelled the meeting on Thursday. Details of those talks hadn't emerged yet.
Mr Kim may see the sit-down with Mr Trump as necessary to easing pressure from crushing sanctions and to winning security assurances in a region surrounded by enemies.
"I just want to mention we're doing very well in terms of the summit with North Korea".
His journey to the United States caps a frenetic few days of meetings between North Korean and American officials. But he repeatedly refused to answer questions on the specifics of how North Korea would relinquish its nuclear weapons or if they would allow global experts to inspect nuclear facilities.
Or, as others wondered, did the reference to master poker-playing signal Trump's recognition that China's Xi was cleverly playing all the cards in his hand, from North Korea and US-China trade issues to great-power relations?
They met with Choe Son Hui, the North Korean vice foreign minister who issued an angry statement last week attacking U.S. Vice President Mike Pence and saying it was up to the United States whether the two sides met in a meeting room or in "a nuclear-to-nuclear showdown".
Kim, who is now ambassador to the Philippines, also served as ambassador to South Korea and was part of the USA negotiating team that last held substantive denuclearization talks with North Korea during the George W. Bush administration in 2005.