Over the weekend, former South Korean diplomat Chang Song-min claimed the North’s leader was in a coma. He told South Korean media: “I assess him to be in a coma, but his life has not ended.”
Mr Chang added Mr Kim’s sister, Kim Yo-jong was being “brought to the fore”.
However, Mr Chang’s claims were met with suspicion by some observers on social media.
Some referred to earlier speculation this year regarding the health of the North Korean leader.
The rumours surfaced following the disappearance of the leader for extended periods of time on a number of occasions this year.
In one occasion in April, Mr Kim was not seen in public for around 20 days.
However, the leader tended to show up again and just this month travelled across the country to inspect areas hit hard by flooding.
Following this weekend’s speculation, one user on Twitter said: “So y’all claimed he’s dead again, for like the third time this year?
“And the source? A former government official of a South Korean president. Someone with no connections, contact, or power in the DPRK or the ROK.”
Another said: “Didn’t we hear similar reports several months ago? Could be fake news. Time will tell.”
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A source told South Korean news site Chosun the dogs were being “forcefully” confiscated and then put down.
They also claimed some dogs were being killed for meat, while others were being sent to zoos.
Mr Kim reportedly said pet ownership was a form of “decadence” and “bourgeois ideology”.
The North Korean leader recently suggested the country’s economy was struggling.
In a meeting with senior officials, Mr Kim said North Korea “faced unexpected and inevitable challenges”.
He also said there had been delays in developing the economy and added living standards had “not been improved remarkably,” according to the Korean Central News Agency.
The country has recently faced floods which damaged hundreds of homes and submerged rice fields, and there have also been fears over outbreaks of coronavirus.
Mr Kim placed the North Korean city of Kaesong in lockdown this month amid fears there may have been a case there, and the country’s Red Cross has sent 43,000 volunteers to help regions prevent outbreaks.
The nation still has not officially reported any cases of COVID-19.