If the trip goes ahead, Ban would be the first UN secretary general to set foot in the North for more than 20 years, and the first international leader to meet Kim since he formally assumed power nearly four years ago, South Korea's Yonhap news agency reported on Monday.
Citing an unidentified high-level UN source, Yonhap said Ban would visit Pyongyang in his official capacity later this week, though no precise dates were given.
"There can't be such a situation where the UN secretary general visits North Korea and does not meet with the supreme leader of the UN member state," the UN source said.
The UN spokesman's office in New York declined to comment on the report, while the South Korean foreign ministry and presidential Blue House both said they were unaware of the visit.
The UN source told Yonhap that Ban was almost certain to meet with Kim Jong-Un -- a meeting which, if it happens, would mark a major diplomatic opening by Pyongyang.
Since taking over the leadership following the death of his father Kim Jong-Il in 2011, Kim has not travelled outside the country.
Ban had been scheduled to visit North Korea in May this year, when Pyongyang invited him to tour the joint North-South Kaesong Industrial Zone, which lies just over the inter-Korean border.
Pyongyang withdrew the invitation at the last minute after Ban criticized a recent North Korean missile test.