The report, however, serves to rebut rumors that she was married to the son of a prominent party official.
In 2014, she ran the country while her brother was incapacitated during a mysterious illness.
The defector reportedly said that an uncle, Jang Sung Taek, had unsuccessfully tried to find a husband for Kim Yo Jong in 2012.
The Sun cites an anonymous North Korean defector as its source for the matchmaking contest tip.
Market Watch parent company Dow Jones is a unit of News Corp, which also owns the Sun.
The story in part echoes quotations and anecdotes reported by a South Korean daily two days earlier.