Choi Soon-sil was detained on October 31, accused of influence peddling and interfering in state affairs.
Eight banks have also been raided in connection with the scandal, South Korean media reported.
The scandal has prompted widespread anger.
Critics say Choi Soon-sil used her closeness to the president to solicit corporate money for foundations she ran, as well as embezzling state funds and directing presidential decisions, despite a lack of office, expertise or security clearance.
Seoul Central District Court will review the request for an arrest warrant for Choi Soon-sil on November 3, a court spokesman said.
President Park Geun-hye has responded by reshuffling her government.
Kim Byong-joon, a senior presidential secretary under a previous administration, was named as prime minister to replace Hwang Kyo-ahn. The role of prime minister is largely symbolic in South Korea, where power is concentrated in the presidency.
Yim Jong-yong, currently Financial Services Commission chairman, was named as the new finance minister and deputy prime minister, replacing Yoo Il-ho.
A new minister of public safety and security has also been appointed.
However, the opposition says the reshuffle is an attempt to deflect attention from Choi Soon-sil.
Surveys show Park Geun-hye’s approval rating is about 10% and about half of respondents say she should resign or face impeachment.
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