Trump has vowed to maintain his approach of "maximum pressure" on the North in the lead up to the talks, claiming they are the reason behind Pyongyang coming to the negotiating table.
The New York Times reported that Trump has asked the Pentagon to prepare options plans for drawing down American troops.
"We now have a date and we have a location".
"Lawmaker Kim said Sunday, "[Holding the summit in Panmunjom] is the best way to guarantee a successful summit while maximising the historic value of the U.S. Kim also pledged to close its nuclear test site this month and invited United States experts and journalists to verify the move. Some 28,500 US forces are based in the allied nation, a military presence that has been preserved to deter North Korea since the war ended in 1953 without a peace treaty.
Trump has indicated that the date and place of the summit have been chosen, and said he believes the Demilitarized Zone that divides the Koreas might be a good venue.
The meeting between the two Korean leaders produced unprecedented scenes, starting with Kim's step over the ankle-high concrete slab dividing the two nations - and then his walk back across the border, hand-in-hand with Moon.
But for Trump to contemplate withdrawing troops now would be a quixotic move as he enters into negotiations with Kim whose demands and intentions are uncertain.
Trump and senior USA officials have suggested repeatedly that Washington's tough policy toward North Korea, along with pressure on its main trading partner China, have played a decisive role in turning around what had been an extremely tense situation.
Mr Trump told the National Rifle Association's annual convention in Dallas on Friday that he had toned down his rhetoric in anticipation of the talks after labelling Mr Kim "Little Rocket Man" past year and threatening him with "fire and fury". It declared North Korea a "world-level politico-ideological and military power" and said it would contribute to building "a world without nuclear weapons".
"There's something I like about it [holding the summit in Panmunjom], because you're there, if things work out there's a great celebration to be had on the site, not in a third-party country", said Trump on Monday.