Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
Here are a few of the top locations being discussed:
It's the only spot along the heavily fortified Demilitarized Zone (DMZ) where North Korean troops stand face-to-face with South Korean and United Nations Command forces.
"Places like Switzerland, Sweden or Jeju Island have been gaining a lot of attention, but we also view the JSA as a serious option," an official with South Korea's presidential Blue House said on Sunday.
Some sceptics see the JSA as a symbol of the Korean War and continued tensions, rather than a place for a peace deal.
However, it would allow Kim and Trump to meet without travelling far from either of their respective security forces or to be seen kowtowing in an "enemy" capital.
Kim is scheduled to meet South Korean President Moon Jae-in at the JSA in April for their first ever summit, and South Korean officials see it as a top contender for a Trump summit as well.
"If North Korea and the US, who are the directly involved parties of the truce agreement, hold the summit at Panmunjom, it would hold the significant meaning of turning a symbol of division into one of peace," the Blue House official said.
Kim Jong Un's father and predecessor, Kim Jong Il, was known to be afraid of flying, but the younger Kim has been shown in official photos getting off airplanes and even "flying" a North Korean designed aircraft.
"In Korea, I'm sticking with Jeju Island. Jeju has soul, born of tragedy, and beauty and nature," said Yonsei University Professor John Delury, who led a discussion of possible summit locations on Twitter.
The island hosts an annual "peace and prosperity" forum in May designed to attract international leaders.
"As the 'Island of Peace,' Jeju is the ideal place to hold the North Korea-US summit," Jeju's governor said in a statement.
Europe
Several spots in Europe, including Switzerland and Sweden, have been raised as possible neutral locations for a summit.
Both countries have international reputations as mediators, and both played a role as members of the Neutral Nations Supervisory Commission helping to regulate relations between the two Koreas after the 1953 armistice that paused - but did not officially end - the Korean War.
As a child, Kim and his siblings attended an elite private school in Switzerland in the 1990s, according to former classmates there. However, Kim's time in the West is not an officially acknowledged part of his biography and analysts say he may want to avoid drawing attention to that period in socialist and impoverished North Korea.
The Swiss foreign ministry has said the country is ready to facilitate talks between North Korea and the United States, and is in contact with both sides.
"It is up to the parties involved to decide if, when and where the talks will be held," the ministry said in a statement.
Sweden's prime minister told reporters on Saturday that the country stands ready to help "in any way."
Sweden has held unofficial talks in the past, and North Korea's foreign minister is expected to visit soon, according to Swedish media.
Asia
A summit in Asia would be closer to home for the notoriously reclusive Kim, and cities including Beijing, Singapore, Hanoi, or even Ulaanbaatar in Mongolia have been raised as possibilities.
Beijing is seen as one of Pyongyang's biggest backers, and has hosted a series of multilateral negotiations over North Korea held intermittently since 2003 and attended by China, Japan, North Korea, Russia, South Korea, and the United States.
In recent years, however, relations between Pyongyang and Beijing have cooled, and analysts say Trump may not be keen on providing a major rival like China a chance to steal some of the limelight.
Mongolia's capital city, Ulaanbaatar, has been the site of past sensitive negotiations with North Koreans, maintains friendly relations with both sides, and has little in the way of political baggage.
Its lack of pizzazz, however, may not provide the backdrop Trump is seeking for his riskiest diplomatic gambit.
Previous meetings between North Korean and American officials have taken place in Pyongyang, including a 2000 meeting between U.S. Secretary of State Madeleine Albright and Kim's father and predecessor Kim Jong Il. Former Presidents Bill Clinton and Jimmy Carter have also travelled to Pyongyang.
However, Albright's trip in particular was criticised for appearing as an endorsement of a brutal and oppressive regime. Any a summit in North Korea - even outside Pyongyang - is seen as a long-shot as any Trump visit would risk similarly unfavourable criticisms of the American president.
Kim could face similar problems travelling to the United States, where no North Korean leader has visited, making many observers think a more neutral setting will need to be found.
Five-time champions hold their nerve to claim victory by nine runs in the final over at Chandigarh
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