The reclusive nation's next leader has been the focus of intense media speculation since Kim reportedly suffered a stroke last summer.
Kim has ruled with absolute authority since Kim Il-sung, his father died in 1994, leading to the communist world's first hereditary power succession.
He has allowed no opposition, raising concerns about a power struggle if he dies suddenly without naming a successor.
The leader has three known sons by two women. The oldest, Kim Jong-nam, was long considered his favourite - until he was caught trying to sneak into Japan using a fake Dominican passport to visit the Disney resort in 2001.
The middle son, Kim Jong-chol, apparently has never been a favourite as a possible successor.