"We need to question the president Tuesday, or Wednesday at the latest," Yonhap news agency quoted an official with the Seoul prosecutors' office as saying, adding they had sent a notice to her office and were waiting for a response.
If Park agrees, she will be the first South Korean president to be questioned by prosecutors while in office.
The scandal centres on Park's shadowy confidant, Choi Soon-Sil, who is accused of using her ties with the president to strong-arm local firms into donating millions of dollars to two non-profit foundations Choi then used for personal gain.
The scandal that emerged late last month has sparked nationwide fury with tens of thousands of taking to the street to call for Park's resignation.
The latest rally yesterday drew one million people, according to organisers, making it the largest public protest in South Korea in nearly three decades.
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