U.S. network CNN cited an intelligence source as saying that Kim was “in grave danger after a surgery”.
The online newspaper Daily NK in South Korea, which specialises in news from North Korea, claimed on Tuesday that Kim was undergoing treatment after a reported cardiovascular system procedure on April 12.
There were also no indications of any “unusual activities” in North Korea.
South Korea’s Unification Ministry said it could not initially comment on the reports.
There was no official comment from North Korea.
The secretive state is not in the habit of disclosing information about its leader, whose age is estimated at 36 in South Korea, or his family.
Kim had attended a key party meeting in the capital Pyongyang on April 11.