Trump revealed last week that two or three locations were under consideration for the historic summit - which would be the first between a sitting United States president and a leader of North Korea - but this is the first time he has publicly named a potential site. "And we are also talking about the possibility of the DMZ Peace House/Freedom House", Mr Trump said.
"It's very simple", Trump said, seeking to strike a balance between optimism and skepticism about his upcoming summit with Kim.
"The United States has never been closer to potentially having something happen with respect to the Korean Peninsula that can get rid of the nuclear weapons, can create so many good things, so many positive things and peace and safety for the world", Trump said.
He said he had raised the idea with Mr Moon, days after dramatic images of Moon meeting Mr Kim at the Peace House dominated the news.
And though, at first, the loud music was considered a nuisance, now K-pop in North Korea is welcome the country's Supreme Leader himself, Kim Jong-un.
Seoul's Defense Ministry said it would pull back dozens of its front-line loudspeakers on Tuesday before media cameras. "North Korea summit, is at a historical turning point", Abe said.
South Korea had already turned off its loudspeakers ahead of Friday's summit talks, and North Korea responded by halting its own broadcasts. It is one of only 47 countries to feature a North Korean embassy.
Traveling to the northern side of the demilitarized zone (DMZ) would also provide a historic opportunity for Trump, the source said, adding that Moon may be involved in the summit in some capacity.
Moon and Kim agreed in their summit to pursue complete denuclearization of the Korean Peninsula and work toward a peace treaty to formally end the 1950-53 Korean War.
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The big guns were back in action on Monday though with the likes of Luka Modric, Marcelo and Sergio Ramos also returning. "I can adapt.
The two Koreas will also set up a communications office in Kaesong in North Korea, although the timing for that was not specified.
His comments come just after a history-making meeting between North and South Korea, where both nations pledged to work towards "complete denuclearization".
As he has said in public, Trump remains insistent he will not be played as the two seek to end the standoff over North Korea's nuclear weapons program. Mr Trump wants to hold it by late May or early June.
Prior to the recent peace talks between North Korea and South Korea, much was made about South Korea's propaganda speakers blaring K-Pop across the border.
"So, we'll see what happens". The summit, in part, took place at the Peace House. USA officials want the North to take complete, verifiable and irreversible disarmament measures.
Jokowi, accompanied by Foreign Minister Retno Marsudi, said he could not confirm whether the offer would be accepted.
China is the North's only major economic partner, but trade has declined by about 90 percent following Beijing's implementation of economic sanctions imposed over the North's nuclear bomb and ballistic missile tests. "This has a chance to be a big event".
King says he thinks North Korea this time is heading in the right direction.