SEOUL—The young daughter of North Korean leader Kim Jong Un appears increasingly positioned to become the rogue nation’s next leader, Seoul’s spy agency said, though Pyongyang itself has stayed mum on succession plans.

Kim Ju Ae, believed to be about 13 years old, has attracted widespread speculation since first appearing in public more than three years ago. She has become a fixture at North Korean events ever since—often referred to in state media as the “beloved child.”

Though her image is ubiquitous in North Korea, Pyongyang has divulged little about the girl. Her full name, age and future role have never been articulated.

Kim Jong Un, who himself just turned 42 years old, is believed to have three children, including an eldest son, according to a 2023 assessment by Seoul’s spy agency. Kim Ju Ae is the middle child. The gender of the youngest child is unknown.

Deciphering whether Kim Jong Un is merely a doting father or a long-term planner is what has drawn intense debate.

On Thursday, South Korean intelligence officials told lawmakers they had spotted indications that Kim Ju Ae was in the stage of being designated as a successor, according to a legislator who attended the closed-door meeting. Previously, the spy agency had said it appeared she had received succession training.

As rationale for the shift in thinking, intelligence officials pointed to the girl attending more marquee military celebrations, as well as a recent New Year’s Day visit to the sacred mausoleum where the embalmed bodies of her late grandfather and great-grandfather, both former North Korean leaders, are on display.

Intelligence officials also saw instances of the daughter offering direct opinions on certain policies during field inspections with her father. The lawmaker who attended the briefing didn’t elaborate, though Kim Ju Ae has been seen whispering in her father’s ear at certain events.

At her first appearance at the ICBM test, she was babyfaced, wearing a white puffer jacket and holding her father’s hand. She barely came up to Kim Jong Un’s shoulders. Since then, her fashion has shifted to more pants, suits and heels. She has grown taller and slimmer—now nearly the same height as Kim Jong Un, who stands about 5-foot-6.

Kim Il Sung, the current leader’s grandfather, founded North Korea in 1950. His successor, Kim Jong Il, wasn’t seen or mentioned in public until his 20s. He then spent two decades as the heir apparent before rising to power in 1994. Kim Jong Un was virtually unknown until a few years before his ascendancy atop the country in 2011.

Write to Timothy W. Martin at Timothy.Martin@wsj.com