The sources declined to be identified given the sensitivity of the matter.
The Liaison Department could not be reached by Reuters for comment late on Friday. China's foreign ministry did not immediately respond to a request for comment late on Friday.
Daily NK, a Seoul-based website, reported earlier this week that Kim was recovering after undergoing a cardiovascular procedure on April 12. It cited one unnamed source in North Korea.
South Korean government officials and a Chinese official with the Liaison Department challenged subsequent reports suggesting that Kim was in grave danger after surgery. South Korean officials said they had detected no signs of unusual activity in North Korea.
On Thursday, US President Donald Trump also downplayed earlier reports that Kim was gravely ill. "I think the report was incorrect," Trump told reporters, but he declined to say if he had been in touch with North Korean officials.