Bringing the Korean War to a formal end 65 years after hostilities ceased will also be on the table at the first-ever meeting between a North Korean leader and a sitting president of its "imperialist enemy".
Those include terminating America's military presence in South Korea as well as ending the US regional nuclear umbrella, a security arrangement in which Washington promises in-kind retaliation on behalf of close allies if they are attacked with nuclear weapons.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee Hsien Loong.
He thanked Singapore's organisation of the summit as if it was "their own family affair".
There has been no indication Rodman would be involved in any official talks at the summit, which is aimed at getting North Korea to give up its nuclear weapons and missiles in exchange for economic incentives and security guarantees.
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It is the farthest Kim has travelled since inheriting power in 2011, and only his third known trip outside the country since then, with the use of a Chinese plane raising questions over the state of North Korea's ageing fleet of Soviet-built aircraft.
Trump descended from Air Force One into the steamy Singapore night, greeting officials and declaring he felt "very good", before he was whisked away to his hotel, driving along a route lined with police and photo-snapping onlookers.
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". China and South Korea would have to sign off on any legal treaty.
Trump advisers cast his actions as a show of strength before the Kim meeting.
North Korea's concept of denuclearization, made clear through years of failed discussions with the global community, "bears no resemblance to the American definition", Evans J.R. Revere, a nonresident senior fellow at Brookings, wrote in a note. Past nuclear deals have crumbled over North Korea's reluctance to open its doors to outsiders. After their initial greeting, the leaders will head into a room for the summit.