The impeachment of the country's President has divided the ruling party and thrown the government into turmoil.
South Korea's ruling Saenuri party has now split, with 29 members forming a new party.
The party's Choung Byoung-Gug called it a new beginning.
"The new conservative party for reform will overcome the pro-Park hegemonism which destroyed the Saenuri party," he said.
"It will start afresh to create a true conservative administration."
South Korea's parliament has been in disarray since it voted to impeach President Park Geun-hye earlier this month.
The President has been accused of colluding with a friend, Choi Soon-sil, to pressure big businesses into paying money to foundations backing the President's initiatives.
Choi Soon-sil is being tried for fraud, but both have denied any wrongdoing.
One of those mooted for the new Presidency is Ban Ki-moon.
But the 72-year-old has so far been non-committal.
"I will really consider seriously how best and what I should and I could do for my country, Korea," Mr Ban has said.
University of Technology, Sydney Korea expert Dr Bronwen Dalton told SBS the outgoing UN Secretary General would be a popular choice.
South Koreans cheer after lawmakers approved the impeachment of President Park in front of the National Assembly in Seoul, South Korea, 09 December 2016. (AAP) Source: AAP
"He has a lot of political capital in that he is admired by South Koreans for his role in the UN," Dr Dalton said.
She said the new party would be working hard to get him on side.
"The conservatives will do all they can to secure his support," Dr Dalton said.
"Because really he is their only chance to keep South Korea governed by conservative politicians."
Ban Ki-moon himself has also been accused of corruption. He has denied allegations of accepting bribes when he was the country's foreign minister.
One of his political rivals, Seongnam City Mayor Lee Jae-myung, has been amongst those airing the claims.
"He will not be able to avoid being heavily doubted if he did indeed use his status to gain personal benefits," Mr Jae-myung said.
"As the time passes he won't be able to maintain the interest and popularity he is enjoying at the moment."
Dr Dalton said the corruption allegations against Mr Ban will be pushed hard by his opposition if he decides to campaign.
"The allegations are quite old (but) in the scheme of things the association between conservative politicians and the chaebol will be his Achilles heel," Dr Dalton said.
"Because South Koreans are very sick of having an economy and a political sphere controlled by these big businesses."
Meanwhile, the country's Constitutional Court has held a second hearing on whether to uphold the President's impeachment.
Lawyers could not agree on the evidence or witnesses to be presented and a third court hearing was scheduled for Friday.
Investigations have also widened to include the chairman of the National Pension Service, Moon Hyung-pyo.
He was placed under emergency arrest after his home was raided.
The special prosecutor's office said he was under investigation for suspected abuse of power.
They have been investigating whether he pressured the pension fund to support the A$11 billion merger last year of two Samsung Group affiliates while he was head of the Ministry of Health and Welfare, which runs the National Pension Service.
