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Trump is scheduled to meet with Moon Sunday, South Korean presidential spokesman Ko Min-jung said Monday.
A White House official, when asked about the DMZ visit, would not comment.
"We're not going into details of the President's schedule yet. There are some things that are still coming together," the official said.
The DMZ is a heavily fortified border that divides the two Koreas, about 30 miles north of Seoul that was established in the 1953 Korean War Armistice Agreement.
Moon and Kim have sought to recalibrate the Joint Security Area as a symbol of peace rather than one of war. The leaders of the two Koreas met there twice last year and vowed to turn the entire DMZ into what they called a "peace zone."
To that end, the two Koreas and the United Nations Command that administers the southern part of the DMZ last year removed all mines from the region and withdrew all guard posts, firearms and ammunition from the Joint Security Area.
CORRECTION: This story has been updated to reflect that Trump is considering visiting the DMZ after the G-20 summit and to clarify that there are no plans for a trilateral meeting between Trump, Moon and Kim, according to a South Korean official.