Secret discussions regarding the planned meeting are taking place as North Korea vice foreign minister Choe Son Hui visits Beijing and Moscow to discuss cooperation.
The Asahi Shimbun reported Thursday speculation is rising that Trump could meet with Kim in Europe, possibly in November.
Trump is expected to attend a Nov. 11 commemoration of the 100th anniversary of the armistice that ended World War I in France.
While in Europe, Trump could travel to Geneva or Vienna, or another third-party country, to hold discussions with the North Koreans, according to the Asahi.
Quoting U.S. and South Korea government sources, the Japanese newspaper also reported the South Koreans offered Seoul as the site of the next summit, but the Trump administration did not warm to the idea.
The Mainichi Shimbun reported Geneva and Vienna are candidate cities for the next summit, and that the U.S. administration is likely to schedule the meeting after the midterm elections in November.
North Korea has gained support for the easing of sanctions from traditional partners China and Russia, and North Korea aircraft are expected to fly to Vladivostok this weekend.
Ahead of the flight, Choe left Pyongyang for China and Russia, according to KCNA.
Japan's Kyodo News reported Thursday Choe could be traveling to exchange views with Moscow and Beijing officials ahead of meetings between Choe and Steve Biegun, the U.S. special representative for North Korea.
Choe could make contact with U.S. officials during the trip, according to Kyodo.