The public prosecutor's office said it was still awaiting information from the South Korean authorities about the offence of which 20-year-old Chung Yoo-Ra is accused, and the possible sentence she faces.
"How long it takes us to reach a decision in the extradition case is partly dependent on when we receive the necessary documents from South Korea," Deputy Director Mohammad Ahsan said in a statement.
Once the documents are received, Ahsan said, prosecutors would make a decision about Chung's extradition "within a few weeks."
Chung was arrested on Sunday night in the northern Danish town of Aalborg for overstaying her visa.
The local district court on Monday ruled that Chung, who denies any wrongdoing, would be detained for four weeks pending the decision on her extradition.
Chung, who has a 19-month-old boy, later appealed to a local high court but the decision to remand her was upheld.
She has the right to appeal against an extradition ruling, and this could prolong the legal process.
Her mother Choi has been dubbed South Korea's "Rasputin." She is a key figure in an influence-peddling scandal that sparked street protests demanding the removal of President Park Geun-Hye.
Choi, 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.