Eighteenth Judicial District Attorney Carol Chambers said Monday that her office is considering pursuing that punishment against James Holmes.
She says a decision will be made after consulting with victims' families.
Holmes made his first court appearance Monday.
After his court appearance, Chambers spoke to the media outside the courtroom.
She told 9NEWS her focus will be to provide the media with as much information as possible while still not tainting the to-be-determined jury pool.
"I would say there's no such thing as a slam-dunk case," Chambers told 9NEWS. "It's a case where we are still looking at the evidence. We will work very hard on this case to prosecute it just like we would any other case."
Chambers says they are a far way away from determining whether the death penalty will officially be on the table.
"The death penalty decision must be made within 60 days of the arraignment," Chambers said. "But, we will be talking with all the victims [until then.]"
Chambers says choosing to pursue the death penalty could be a long, painful process for the victims.
The 24-year-old former graduate student is being held on suspicion of first-degree murder.
Holmes is suspected in a shooting at a theater in a Denver suburb that killed 12 people and injured 58.
(KUSA-TV © 2012 Multimedia Holdings Corporation with The Associated Press)