Trump has clearly ruled out key cities like Pyongyang, Seoul and Beijing, and may stay away from the truce village of Panmunjom straddling the North-South border, according to the report.
Cities in northern Europe where North Korean officials attended quickly arranged meetings stay under consideration, as well as locations in Southeast Asia, where both the United States and North Korea retain embassies.
In Asia, Bangkok, Singapore and Ulaanbaatar are candidate cities.
A summit in Mongolia could allow Kim to travel by armored train, according to Bloomberg.
North Korea media has mostly stayed away from addressing the summits until this week.
The Rodong Sinmun stated in an article published Wednesday the "2018 North-South Summit" is to be a "noteworthy event for the unification of the Fatherland."
Kim's "firm will for unification" is reflected in the decision to hold the summit, state media claimed Wednesday.
The day North Korea's will to unify the peninsula is "coming to light," and will be realized, the article added.
The summit between Kim and South Korean President Moon Jae-in, to be held in Panmunjom on April 27, will be broadcast live.
The meeting was not officially acknowledged in state media until April 9, and Pyongyang has yet to publicly acknowledge the planned summit with Trump.