The police requested the prosecution to apply for a writ against the 33-year-old Park over his suspected drug use, after quizzing him on three occasions.
He is alleged to have used methamphetamine early this year with Hwang Ha-na, the now arrested granddaughter of the founder of Namyang Dairy Products Co.
Hwang, 31, was arrested earlier this month on charges of buying methamphetamine and using the illegal substance in 2015. She reportedly told police that she was lured by Park into using drugs together.
Police called in Park last Wednesday for the first time. He has flatly denied the allegations.
Police earlier obtained CCTV footage showing Park picking up something about 20-30 minutes after probably sending money to a bank account suspected to belong to a drug dealer via an ATM in Seoul.
He told police he sent the money at the request of Hwang but claimed he did not use drugs.
Hwang was Park's fiance. The couple planned to get married in 2017 but broke up the following year.
A court hearing to review whether to arrest Park will be held as early as Wednesday. (Yonhap)