South Korean prosecutors have also reportedly questioned heads of some large scandal-related conglomerates.
The list includes chairman of Hyundai Motor, Chung Mong-koo. Prosecutors also plan to summon the de facto head of Samsung Group, Jay Y. Lee.
The Yonhap news agency says the investigation focuses on whether the president exerted pressure on the bosses to raise funds for two foundations involving her friend Choi Soon-sil.
Last week prosecutors raided Samsung Electronics on suspicion it separately gave millions of euros to a company controlled by Choi.