(BBC News)
South Korean reports say that Kim Yong-chol, flying from Beijing, is carrying another letter from Mr Kim to Mr Trump.
He is expected to meet US Secretary of State Mike Pompeo on Friday, South Korea's Yonhap news agency said.
Speculation is mounting that the second summit could be held in Vietnam.
The North Korean leader is scheduled to travel to the communist-run country for an "official state visit" sometime in February, Reuters news agency is reporting, citing unnamed sources.
Little progress has been made on North Korean de-nuclearisation since a historic meeting in Singapore last June between Mr Kim and Mr Trump.
But there has recently been a flurry of diplomatic activity. Mr Kim visited China earlier this month for talks with President Xi Jinping, as he did before the Singapore summit.
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