Environment Minister David Spiers is also a contender for the position.
State Premier Steven Marshall spoke candidly about the two candidates and the path forward.
"So let's wait and see what happens. But already two excellent candidates have put their names forward," Mr Marshall said.
"I strongly respect the great strengths of both Dan van Holst Pellekaan and David Speirs. They've both got senior roles within my cabinet, within the government.
"I'd be very pleased with either of those who have nominated so far."
The opposition member Stephen Mullighan says there are more pressing matters that should have the Liberal's attention - in particular South Australia's battle into a COVID-normal life.
"Today the Liberal Government will be spending its time focusing on who's going to get the plum job of Deputy Premier, after the resignation of Vickie Chapman," Labor's Mr. Mullighan said.
"Now is exactly the time when South Australian's need a government focus on getting us out of COVID, and making sure the health system is ready."
Get the latest breaking news from SCA newsrooms around Australia. Short, simple and everything you need to know.