The official was not authorized to speak publicly about internal deliberations and insisted on anonymity.
"If the summit becomes a success, the Singaporean efforts will go down in history", Kim said.
One dispatch by the Korean Central News Agency said North Korea and the United States would exchange "wide-ranging and profound views" on establishing new relations, building a "permanent and durable peace-keeping mechanism", achieving denuclearization and "other issues of mutual concern, as required by the changed era".
The report notes the summit is being held "under the great attention and expectation of the whole world".
Trump on Monday morning broke into a Twitter tirade about trade directed at America's European allies with the upbeat message: "Great to be in Singapore, excitement is in the air!".
Mr Lee also said it was "not easy" to find a location in the world that is suitable to host such a high-level meeting.
The meeting between Donald Trump and Kim Jong-un is being considered as a major step towards the denuclearisation of the so-called "nuke-bound" nation, North Korea. As a part of that process, he also announced a suspension of nuclear and missile tests and the dismantlement of a key atomic testing facility that was carried out last month.
Kim held a meeting with Singapore Prime Minister Lee Hsien Loong ahead of the planned summit.
While en route to Singapore, Trump said he looked forward to meeting Kim on what he anticipated would be an exciting day.
Trump descended from Air Force One into the steamy Singapore night, greeting officials and declaring he felt "very good" before being whisked away to his hotel via a route lined with police and photo-snapping onlookers.
Kim met with Lee on Sunday.
U.S. Secretary of State Mike Pompeo, who is also in Singapore, said in a tweet that Washington was "committed to the complete, verifiable, irreversible denuclearisation of the Korean peninsula".
Last year, the North made one of the biggest breakthroughs in its missile and nuclear weapons programs - which it says it needs to defend against the risk of a USA invasion - when it announced that it had "completed" its state nuclear program after testing a missile capable of striking most, if not all, of the continental U.S.
Pope Francis has prayed that the summit this week between the USA and North Korean leaders succeeds in laying the groundwork for peace. For the North, Kim Jong Un has already won a huge propaganda bonus by merely having the summit and sitting down as an equal with the USA president, an accomplishment his father and grandfather sought but could never realize. Francis said he wanted yet again to send "a special thought in friendship and prayer" to the beloved Korean people.
Kim arrived with Kim Yong-chol, his right-hand man and Foreign Minister Ri Yong-ho.
It's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
"The entire world is watching the historic summit between [North Korea] and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
Kim Jong Un met Singapore Prime Minister Lee Hsien Loong shortly after his arrival, driving from the St. Regis Hotel where he is staying, through the famous Orchard Road shopping district, which was closed off for his tightly guarded motorcade.
The two leaders meet at 9am (1100 AEST) on Tuesday at the Capella on Sentosa island, a refurbished British Army artillery mess that is now one of Singapore's most expensive luxury hotels.
The talks have been portrayed by Trump in recent days more as a get-to-know-you session.