Chung Yoo-Ra, the 20-year-old daughter of the woman dubbed South Korea's "Rasputin", is one of the figures in the influence-peddling scandal that sparked massive street protests demanding the removal of President Park Geun-Hye.
Chung was detained in Denmark almost a month ago for overstaying her visa, after South Korean authorities issued a warrant for her arrest. Seoul then sought her extradition.
The Danish Office of the Director of Public Prosecutions said the Aalborg district court had on Monday granted it more time to complete its processing of the case.
"We have asked the Korean authorities to answer some follow-up questions. Until we receive these answers, we cannot reach a decision on the question of extradition," the office said in a statement.
It said it believed it would take "some weeks to reach a decision after the information is received from the Korean authorities."
Chung has denied any wrongdoing. The equestrian, who has reportedly bought horses and trained in Denmark in the past, has told police that she was in the country due to her involvement in the sport.
Chung's mother, a confidante of Park, is accused of using her influence to secure her daughter's admission to an elite Seoul university, with a state probe revealing the school had admitted Chung at the expense of other candidates with better qualifications.
The revelation touched a raw nerve in education-obsessed South Korea.
Several professors at Ewha Women's University, including a former school president, have been investigated for allegedly giving Chung preferential treatment.