He adds that at some point he'd like to invite Kim to the United States.
When the leaders of North and South Korea had their historic meeting in April, North Korea's Kim Jong-un asked for help with updating his country's railways, which he said were in an "embarrassing" state.
Trump said they had discussed three sites for the summit but had not decided anything, adding that he was open to receiving Kim in the U.S. at some point, reports Efe news.
Rather than requiring a declaration of nuclear weapons sites as a prerequisite to a second meeting with Trump, Pence told NBC News that the administration will insist on developing a "verifiable plan" to disclose those sites while the two leaders are in the same room.
The President's comments came hours after Trump and Chinese President Xi Jinping held a working meeting in Argentina, discussing several issues that included a temporary freeze on higher tariffs, fentanyl reclassification as a controlled substance, and the North Korea peninsula.
Prospects for a second summit to overcome a current logjam in negotiations will likely depend on whether either the US or DPRK can show flexibility with regards to offering gestures surrounding sanctions relief or steps towards denuclearization.
North Korea was angered by Washington's refusal to ease sanctions and warned it could resume its nuclear programme.
It marked the first time in a decade that a train from the South entered North Korea.
Storm Diana set to bring high winds and heavy rain to Hartlepool
He added: "Storm Diana has been named by Portugal's IPMA as a result of impacts on the Azores". Storm Diana, named by Portugal's IPMA weather service, is now threatening the Azores.
Fed: Slower pace of monetary tightening? - Westpac
In November, Fed policymakers agreed to hold rates steady, leaving the benchmark rate unchanged in a range of 2% and 2.5%. After the financial crisis erupted in 2008, the Fed kept rates at historically low levels to revive the ailing economy.
Jahana Hayes says she supports Pelosi for house speaker
Jeffries said the caucus will be "member-driven" and focus "like a laser beam" on making sure they have a successful two years. Ms Pelosi was the first woman to be speaker when Democrats had the House majority from 2007 to 2011.
They agreed on the need for "maintaining vigorous enforcement of existing sanctions to ensure the DPRK understands that denuclearisation is the only path", Sanders said, using the North's official name, the Democratic People's Republic of Korea.
They have begun work to reconnect their railway systems, removed landmines and destroyed military bunkers at parts of the frontier.
They have also begun work to reconnect a train line and fix another rail link across the border.
In their most recent summit in Pyongyang in September, Kim and Moon committed to reviving economic co-operation when possible, voicing optimism that worldwide sanctions could end to allow such activity.
"We're getting along very well, we have a good relationship", Trump also said.
Moon agreed to enhance bilateral efforts to denuclearize North Korea after meeting with Dutch Prime Minister Mark Rutte on Saturday.
The prospect of Kim's visit to Seoul had been in doubt amid the stalled denuclearization talks between Pyongyang and Washington, with the two sides in a deadlock over who should make the first move since Kim and Trump held their first summit in June.