The meeting is set to take place Tuesday morning (Monday evening Washington time), when the leaders will talk one-on-one.
Depending on how the talks go, Trump has signalled the summit could collapse quickly or stretch into future meetings and perhaps even include a follow-up encounter at his Florida golf club, Mar-a-Lago.
In a statement, US State Secretary Mike Pompeo said "The president is well-prepared for tomorrow's engagement with Chairman Kim".
"We will take actions to provide them sufficient certainty that they can be comfortable that denuclearisation is not something that ends badly for them", Pompeo said.
He is one of the few westerners to have met the North Korean leader on visits to the capital city Pyongyang. A second round of meetings was planned for the afternoon as officials worked to lay the groundwork for progress to be made Tuesday, according to the official familiar with the preparations.
It was a striking about-face from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged US dotard".
"The nuclear testing has got them to the point where they now get this meeting", he said. At 4pm, Trump is scheduled to talk to the media and leaving Singapore at 7pm. "We were able to complete the preparations for the historic summit, and I would like to thank you for that", Kim, speaking through an interpreter, told Lee.
Image credit ULI-PwC report
Victor Cha, who was director for Asian affairs at the National Security Council under President George W. Bush, said the "likely reality is that the summit will produce something in between these two extremes". After the meeting, this could make it hard to verify what's said and whether any promises were made.
"I don't think it's fair to raise people's expectations unnecessarily", he said. He told reporters he thinks he will know nearly immediately whether a deal can be made, saying: "I will know, just my touch, my feel".
The fact that Trump agreed to meet Kim without preconditions is hugely significant.
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome.
"Among the positive steps that you can commit to right away are: pledges or agreements to formally end the 68-year war, ending the practice of U.S".
Pompeo, who has traveled twice to Pyongyang to meet with Kim, told reporters Monday that North Korea has conveyed a willingness to denuclearize.
The White House said it does not believe there is any cause for concern about getting an accurate description of the two men's words.
Trump, asked last week if Rodman had been invited to Singapore, said, "No, he wasn't".
Trump withdraws endorsement of G7 joint statement, slams 'weak' Trudeau
Was it really "socialist"? "They're also anxious about the retaliatory measures that we will take". I suspect the personal will also be more fascinating than the political in Singapore this week.