Oh Hyun-joo, a deputy director of national security for the South Korean presidential office, told reporters that she did not have concrete information, despite speculation in the media, about a meeting between the two leaders as Trump visits Asia.
Trump has said he is open to meeting with Kim.
During his visit to South Korea this week, Trump is set to hold a summit with South Korean President Lee Jae Myung on the sidelines of the Asia-Pacific Economic Cooperation events.
Washington and Seoul are seeking to finalise a preliminary trade deal reached with Trump in July, after their first summit meeting in August ended without an agreement.
After three rounds of trade negotiations this month, South Korean negotiators suggested in recent days that the two countries have yet to reach an agreement on the details of a $350 billion investment package, which is included in the pact, despite some progress in narrowing differences of opinion.
Oh, the presidential adviser, added she found it unlikely to see any final trade deal being reached during the Lee-Trump meeting this week.
