According to Yonhap News Agency, Vietnam has been suggested as the venue for the meeting.
Talks of holding a second summit come amid stalled denuclearisation talks between the US and North Korea.
Even though engagements between Washington and Pyongyang reached new heights in 2018 with the Singapore meeting between Trump and Kim in June, the last few months of the year saw a stalemate in relations.
Progress after the June summit has been slow since North Korea eyes sanctions relief while the US insists that the sanctions remain intact.
Kim, in his New Year's speech, had threatened that his country would have to "seek a new way" if the US "does not make good on its promises" with regard to denuclearisation and continues with sanctions.
However, the US President has remained firm that sanctions will remain "in full force and effect.
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