Cunanan was a charismatic character from the San Diego gay-bar scene who went on a cross-country killing spree a decade ago, ultimately killing fashion designer Gianni Versace outside his Florida home before killing himself.
The creators of the new show said they want to use the Cunanan story to examine the U.S. obsession with celebrity culture.
"I felt it was symptomatic of a bereftness in our individual lives, that we kept looking obsessively at the parade of short-term attention-grabbers flitting by on 'Entertainment Tonight,'" Mark Bennett told the Los Angeles Times.
"The tricky part is finding out just what that way would be, finding a structure for the story, and the right people to work with and really explore it."
Bennett has been working on the show along with Jessica Hagedorn and Michael Greif for about six years in between other theater projects.