Quinn's administration wants to close Dwight Correctional Center and Tamms Super Max in Southern Illinois, along with other facilities.
He says the prisons are too expensive.
Union workers filed a lawsuit against the move.
In response, a judge extended the transfer of inmates until August 31st.
Quinn wanted the prisons closed by then.
But he tells WMBD 31 the closures will happen.
"I am confident we'll be able to get this closure done. It's not easy, but it's necessary if we're gonna save taxpayers money and do things right for education, healthcare, and public safety," says Quinn.
A hearing on the matter is set for August 31st.