Park, 65, had her removal from office confirmed by the country's top court earlier this month, ending her executive immunity, and her prosecution has been a key demand of the millions of people who took to the streets to protest against her.
The former president is accused of multiple offences including bribery, leaking government information, and abuse of power in the scandal.
"The accused abused her enormous power and status as president to receive bribes from companies or to infringe upon the rights to freedom of corporate management and leaked important confidential information on state affairs. These are grave issues," the prosecutors said in a statement.
"A large amount of evidence has been collected so far but the accused is denying most of the charges, and there is a risk of destroying evidence in the future."
Her secret confidante and alleged accomplice Choi Soon-Sil is already on trial, and prosecutors said it would be "counter to the principle of fairness" if Park was not arrested.
The statement did not make explicitly clear whether they had already applied to the Seoul Central District for an arrest warrant.
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