South Korean authorities said on Tuesday they will proceed with steps to extradite Chung Yoo-ra, the daughter of a central figure in a South Korean political scandal that has led to a parliament vote to impeach President Park Geun-hye.

Chung is being held in Denmark after police there arrested her on Sunday in the northern city of Aalborg. Denmark's public prosecutor said on Monday that Chung will remain in custody for four weeks after having been charged with committing economic crime in South Korea.

Chung is the 20-year-old daughter of Choi Soon-sil, a friend of Park accused of colluding with the president to pressure businesses to contribute to non-profit organizations. Both have denied any wrongdoing.

"Chung has said she is willing to return to South Korea in three days if she is set free upon entry, which the government has declined to accept," South Korea's special prosecutor's office said in a statement.

It added there is a chance Chung, an equestrian competitor who trained in Germany, may choose to return to South Korea voluntarily.

The scandal has drawn hundreds of thousands of protesters onto the streets of Seoul for weekly demonstrations and could result in Park, 64, becoming the first democratically elected South Korean leader to leave office early.

Park was impeached by parliament late last year, a decision that must be upheld or rejected by the Constitutional Court. Arguments were set to begin on Tuesday in a court process that could take several months.

Meanwhile, South Korea's ambassador to Denmark delivered a letter of intent to Chung to cancel her passport, South Korea's Yonhap News Agency reported on Tuesday, citing unnamed diplomatic sources.

As a result, Chung's passport will no longer be valid after January 10, Yonhap said.

Chung's lawyer could not immediately be reached for comment.