South Korean lawmakers defecting from the ruling Saenuri Party said Tuesday they would soon launch a new political party and hoped the outgoing United Nations Secretary-General Ban Ki-moon would join them. The lawmakers are hoping Ban would agree to run for president as part of their new party.

The Saenuri Party is embroiled in a political controversy — South Korea’s biggest in recent years — with President Park Geun-hye, a member of the ruling party, at the center of a corruption scandal that led to a parliamentary impeachment vote against her earlier in December.

Twenty-nine lawmakers, who will join the new party, also voted in favor of Park’s impeachment.

“We are hoping Secretary-General Ban Ki-moon will join the New Conservative Party for Reform, and if he joins, it will be right that he would compete in a fair primary,” Yoo Seong-min, a member of the new party and a possible presidential candidate, reportedly said using the party’s tentative name.

Park, who is still president in name, allegedly allowed her friend Choi Soon-sil to meddle in government affairs. Choi allegedly influenced Park’s decisions and used her ties to the president to amass profits. Both Park and Choi have denied any wrongdoing.

The nation’s Constitutional Court said Tuesday official hearings regarding the impeachment of Park would begin next week. Following the parliament’s Dec. 9 vote, the court has up to six months to either dismiss the charges against Park and reinstate her as president or fall in line with the parliament’s decision.

If the court approves the parliament’s impeachment vote, fresh elections must be held within 60 days.

Ban has not officially announced his bid for presidency but said he would devote himself to his country after he finishes his second term as the U.N. chief. The 72-year-old served as South Korea’s minister for foreign affairs from 2004 to 2006 and will return to the country on Jan. 15, 2017.

“I will devote my whole body to work hard if what I have seen and experienced as the U.N. secretary-general helps develop the Republic of Korea,” Ban told Korean media last week. “I will decide what to do after meeting people from every walk of life after returning home.”

A new poll indicated that popular support for the U.N. chief in his home country had risen by 2.8 percent last week. Ban is currently enjoying a slim lead over other potential presidential candidates.