Officials from the South Korean intelligence services said they were looking into a CNN report that said the North’s leader was “in grave danger”, citing unnamed US intelligence sources.
An earlier report by Seoul-based news outlet Daily NK said Mr Kim was staying at a countryside villa outside Pyongyang while he recovered from heart surgery, and that his condition was improving.
The South’s Unification Ministry, which handles affairs relating to North Korea, said it could not confirm either report but was investigating the matter.
But a government source told the Yonhap news agency that South Korea was yet to see any “unusual signs” coming from the North regarding Mr Kim’s health condition.
Speculation about the state of Mr Kim’s health has grown since he was conspicuously absent from events on 15 April commemorating the birth of his grandfather Kim Il-sung, the founder of the nation.
The date is a national holiday and one of the most important in the North Korean calendar. Dozens of top officials attended a flamboyant military parade at the Kumsusan Palace of the Sun, Kim Il-sung’s mausoleum, but Mr Kim was nowhere to be seen.
It is notoriously difficult to glean information about the closed-off country or its dictatorial leader other than what little is proclaimed by the North’s state media.
Mr Kim’s movements were last reported in KCNA, the country’s official news agency, on 11 April, when he chaired a meeting of the ruling party’s politburo.
His absence from the 15 April events led to speculation at the time that he might be attempting to distance his own rule from the legacy of his grandfather – or perhaps that he had been struck down with coronavirus. North Korea has officially declared zero Covid-19 cases, a claim met with scepticism by experts.
It is not the first time Mr Kim’s health has been a matter of speculation. In 2014, he disappeared from the public eye for more than a month – and then was pictured using a cane on his return. South Korea’s spy agency said he had undergone an operation to remove a cyst from his foot.
Duyeon Kim, a North Korea expert at Crisis Group, noted that Mr Kim wasn’t the first North Korean leader to be subject to such reports. “We’ve been here with his father and grandfather and were wrong too many times before,” she said. “It’s easy to speculate.”