Kim's failure to appear at North Korea's 60th anniversary parade on September 9 sparked widespread conjecture that he was ill or even dead.
South Korean officials have said that he underwent brain surgery following a stroke around mid-August. Some reports said that Kim has suffered partial paralysis.
However, North Korean state television last week broadcast photographs which it said were of a recent inspection by Kim of a women's artillery base.
"We've heard the news. We are checking it," a spokesman for South Korea's National Intelligence Service said of Saturday's reports. He declined to say whether the spy agency had learned of the expected announcement from Yomiuri Shimbun or a different source.
Dr Pavel Felgenhauer, a Moscow-based military analyst, told Al Jazeera that there would likely be a power struggle in North Korea if it was announced that Kim had died.
"When the father of Kim Jong-il died there was a smooth transition because there was a clear heir to the throne, now there isn't and there is a high possibility of a destabilisation of Korea," he said.
"There are the military leaders who are very powerful, there is also the Kim family that is very powerful, clearly there are going to be divisions."
Kim Jong-il 'in control'
South Korea's defence minister said on Friday that he believed that Kim remained in control in Pyongyang despite the widespread reports, but that the situation in North Korea was unpredictable.
|Kim's absence from the country's 60th anniversary parade sparked rumours [EPA]
"Kim Jong-il has not been seen in public for a while now, but both Korean and United States intelligence services estimate that he still has control over his administration," Lee Sang-hee told reporters in Washington.
Lee, joined by Robert Gates, the US defence minister, said that Washington and Seoul were monitoring the situation closely.
He said the state of Kim's health had "significant implications for the security of the Korean peninsula.
"Crisis or instability situations in North Korea could stem from many different causes, so it would be very difficult to predict them at this point," he said.
On Thursday, Pyongyang threatened to end all relations with Seoul, a major source of aid and cash, in anger at moves by Lee Myung-bak, South Korea's president, to cut off much of the largely unconditional aid it provides.
Analysts say that North Korea may feel that it is able to sever its connections with the South because of leverage gained by its renewed commitment to dismantling a nuclear plant.
"For North Korea right now reunification right now would be like the reunification of Germany; the disapperance of a Stalinist communist state, and of course the leadership is totally against that," Felgenhauer told Al Jazeera.
"There could be again a crisis between the South and North, although hopefully this will just be the closing of borders and in a year or so they will go again for some kind of detente."