Choi was taken into custody and stood trial over a string of corruption allegations, including bribery and closed-door intervention in state affairs.
The imprisonment demand was for Choi's wrongdoing to allow her daughter to receive illegal academic favors at Ewha Womans University in Seoul.
A Seoul court, tasked with the trial of Choi's case, decided to combine Choi and Park's cases together. Prosecutors had yet to demand the penalty against other corruption charges of Choi and Park.
If convicted of bribery, Choi and Park would face at least 10 years in prison.
Chung Yoo-ra, Choi's daughter, arrived at Incheon International Airport, west of Seoul, on Wednesday afternoon. The 21-year-old was extradited from Denmark where she was in custody for about five months.
She repeatedly refused the summons by South Korean prosecutors for her alleged involvement in the corruption allegations surrounding her mother.
The Danish court decided to extradite Chung, but she appealed the ruling. She withdrew the appeal last week.
Prosecutors were expected to seek an arrest warrant for Chung for questioning. Chung was suspected of receiving illegal finance assistance from Samsung Group, the country's biggest conglomerate, for her equestrian training.
