Park is accused of having allowed close friend and confidante Choi Soon Sil to meddle in state affairs.
According to media reports, the head of the main opposition Democratic Party, Choo Mi Ae, and the leaders of two smaller opposition parties met and renewed their demand for Park’s unconditional resignation.
The parties agreed to put an impeachment vote to parliament on Friday; however the vote might be pushed back one week.
As a two-thirds majority is required for the impeachment vote to be successful, votes from members of Park’s own Saenuri Party would be required.
Park is accused of having allowed close friend and confidante Choi Soon Sil to meddle in state affairs and of giving her access to official state documents, even though Choi has no official state position.
On Tuesday, Park once again apologised for the scandal and said she would be prepared to resign as president but would let the parliament decide her exact political fate.
Park who has being in power since February 2013, saw her approval rating drop recently to 4 per cent.
Report says her five-year term is set to end in February 2018, with elections in December 2017.