North Korea has not confirmed who the woman is but, quoting an unnamed government source, a South Korean news agency said the mysterious lady was highly likely to be Mr Kim's wife.
Last week South Korean intelligence sources named the attractive, short-haired woman as Hyon Song-wol, who used to front the Bochonbo Electronic Music Band and was hugely popular among the North Korean masses.
There are reports that 28-year-old Kim Jong-un was ordered to break off his relationship with Hyon by his father Kim Jong-il, and that she later married an officer in the North Korean army with whom she has a baby.
On Sunday's visit to the preschool, she stayed close to Mr Kim while other officials were standing a few steps further away.
Contains footage from Reuters
