A Senate panel is expected to move the bill forward Monday. The House passed the measure in a 57-1 vote in early March.
The measure seeks to include digital books under material protected by the state law that prohibits the disclosure of public library records.
Officials who release information about someone’s requested or checked out library material face misdemeanor charges in Arizona.
The law does allow library records to be accessed if required by law or a court order.
Digital publishing has become increasingly popular in recent years. The Association of American Publishers reported 3.4 million ebooks were sold in 2011.
Library officials nationwide say more people are requesting ebooks.