"Chung has made up his mind to offer his resignation to President Moon Jae-in next week when he returns from a visit to the Middle East," said a source who asked not to be named, Yonhap News Agency reported.
Hung is scheduled to visit Tehran to close the negotiations with Iranian officials regarding a South Korean ship that was seized by Iran over three months ago.
The source said it has not yet decided whether the former parliamentary speaker will immediately return to the party or resign after parliament endorses his successor.
Among the lineup of potential successors are former Interior Minister Kim Boo-kyum and Lee Tae-bok, who previously served as a health minister.
Chung, 69, is the second prime minister under the Moon administration, succeeding Lee Nak-yon who was the longest-serving prime minister in South Korea.
Chung is one of the potential presidential candidates from the ruling party, trailing behind Lee and along with other politicians, such as Kim and Rep. Park Ju-min.
RHM/PR