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.
"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.
Park could respond as early as Tuesday after she appoints a lawyer to represent her, her spokesman said without elaborating further.
If Park agrees, she will be the first South Korean president to be questioned by prosecutors while in office. She had earlier vowed not to hide behind presidential privilege if required to give testimony.
