It is also unclear whether US officials will raise human rights issues in meetings with the North Koreans.
KCNA's coverage also highlighted Mr Kim's late-night stroll in Singapore, and said the leader was impressed by a "nocturnal bird's eye view" from the top of the Marina Bay Sands hotel, where a SkyPark links three 55-storey towers.
Last week, Rodman said he would "give whatever support is needed" to his "friends" Trump and Kim.
It will be the first-ever meeting between the leaders of the USA and North Korea.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee.
Still, the sense of anticipation was great in Singapore, with people lining spotless streets holding cellphones high as Trump headed to meet Lee.
Some foreign-policy experts said the breakdown at the Group of 7 meeting would play to North Korea's advantage, since Mr. Trump can ill afford a second failed summit, back to back.
"We've got a very interesting meeting. tomorrow, and I just think it's going to work out very nicely", Trump said on Monday.
While Trump and Kim search each other's eyes and words for signs of trust or deceit, the rest of the world will be watching, hoping that somehow these two unpredictable leaders can find a way to defuse one of the planet's most unsafe flashpoints.
Kim was not believed to have left his hotel since a meeting with Singapore Prime Minister Lee Hsien Loong soon after his arrival in the city on Sunday, but he ventured out on Monday evening. As I recently wrote, while certain sanctions on North Korea are discretionary, a key 2016 law specifically obligates the president to sanction people and entities complicit in human rights abuses in North Korea - not just those involved in weapons proliferation - and the Trump administration legally can't suspend sanctions more broadly unless North Korea implements key human rights reforms.
Since then, he's launched almost 100 missiles and conducted North Korea's most powerful nuclear tests.
It's unclear what Trump and Kim might decide Tuesday.
Pyongyang has said it is willing to deal away its entire nuclear arsenal if the United States provides it with reliable security assurances and other benefits.
But when pressed by reporters, the secretary of state would not say whether or not that could include reduction of the number of or removal of US troops in South Korea.
He went out of his way to be cordial during two summits with South Korean President Moon Jae-in in April and May. Speaking to reporters on Monday, Rodman suggested that he may have played a role in making the world pay attention to North Korea.