Mr Trump told reporters aboard Air Force One on his return from the G-20 gathering in Argentina that he thinks the meeting will be in early 2019.
"We're getting along very well. We have a good relationship", Mr Trump said, adding that at some point he will invite Mr Kim to the US.
Talks on a follow-up to the two leaders' first meeting in June in Singapore have been underway since July, a senior US official told Reuters in October.
South Korean President Moon Jae-in arrived in Auckland on Sunday on a state visit that will include his summit with Prime Minister Jacinda Ardern.
Ukrainian leader calls on North Atlantic Treaty Organisation to send warships after clash with Russian Federation
The peninsula existed as a semi-autonomous region of Ukraine, with political bonds to Kyiv but strong cultural ties to Moscow. Russian state-run media said Friday Moscow isn't planning a counter-ban for Ukrainian men of military age.
Seoul plans to hold a groundbreaking ceremony before the end of the year on a plan to establish road and rail links between the two Koreas, first agreed upon by the countries' two leaders at a summit in April.
South Korean officials planned to debrief him to try to determine his motive for defecting, the military said.
The two leaders signed a vaguely worded document on denuclearisation of the peninsula, but progress since has stalled as Washington and Pyongyang spar and North Korea has taken few concrete steps to abandon its nuclear and ballistic missile programs.
It is the first time since 2007 a train from the South has entered North Korea.
Draper in space race for $2.6b in NASA moonshot contracts
Working with US companies is the next step to achieving long-term scientific study and human exploration of the Moon and Mars . These companies will be developing small launch vehicles and robotic rovers over the next 10 years.
The US has given its support to the rail survey, but Mr Moon will have to have a number of hard conversations if he's to persuade President Donald Trump that easing sanctions at this stage would be worthwhile so the project can go ahead, our correspondent says. That original plan was botched by Washington's reluctance to lift sanctions on the North until last week, when it finally gave the green light.
They have begun work to reconnect their railway systems, removed landmines and destroyed military bunkers at parts of the frontier.
- Kim visit to Seoul this year? The inspections are preparations for a project to connect the railways of the Koreas, as agreed between leaders of the South and North at their summits this year.
But prospects of a fourth Moon-Kim meeting have recently dimmed, with negotiations on denuclearizing the North grinding to a halt. While the USA insists on allowing inspectors to verify Pyongyang's commitment to the agreement, North Korea wants Washington to act in good faith and lift some of the sanctions.
Priyanka Chopra and Nick Jonas have officially gotten married
The Jonas and the Chopras, including the bridesmaids and the groomsmen, also wore Ralph Lauren couture for the ceremony. People magazine said the ceremony was officiated by Jonas's father Paul Kevin Jonas.
The two leaders made a vague commitment on "denuclearization" of the Korean Peninsula during the summit, but glossed over how to make it happen.