The White House hasn't said whether Trump is willing to place US troop levels on the negotiating table when he meets with Kim.
The Times report, which cited several unidentified officials briefed on the deliberations, said reduced troop levels were not meant to be a bargaining chip in Trump's upcoming summit with Kim.
Leader Kim Jong-un promised the move during the meeting at Panmunjom in the Demilitarized Zone that divides the peninsula, when he and the South's President Moon Jae-in pledged to pursue denuclearisation and a peace treaty.
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Washington has been able to secure the release of its citizens in the past but banned Americans from visiting the North after college student Otto Warmbier's death soon after being returned to the U.S.in a comatose state a year ago.
"The trip is being scheduled", Trump said. "We'll be announcing it very soon", Trump said from the White House lawn. "But if a peace treaty is signed, the USA troops are bound to peter out".
Trump has praised his Chinese counterpart Xi Jinping's efforts on North Korea, calling them a "great help".
According to its website, North Korea's state-owned carrier Air Koryo flies to cities in Russian Federation and China, two countries that maintain diplomatic relations with Pyongyang.
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Earlier this week, the United States president suggested that the demilitarised zone, or DMZ, between North and South Korea would be an excellent venue for the planned summit, but that Singapore was also a possible site.
President Trump did not share details on the time and place for the landmark meeting with Mr Kim.
"A lot of things have already happened with regard to the hostages", Trump said.
The media said the move is the first practical step for national reconciliation and unity between the 2 Koreas since the inter-Korean summit late last month.
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The deal must prevent Iran from becoming a nuclear threat, with stronger provisions in place to force them to keep their word. The report says two US officials believe that the shipments are intended for Iranian ground forces that would attack Israel.