Topinka died last week. The Republican had won a second term, which starts next month.
In a legal analysis released Monday, Madigan says Quinn should appoint someone until Jan. 12, when the current term ends and new elected officials are sworn in. Then once Rauner is in office he should appoint someone.
But Madigan says it's an elected office. She says voters should have a say in a replacement as early as possible.
A spokesman says Quinn is reviewing the analysis.