Detectives with the Los Angeles Police Department's North Hollywood Division said they will name the suspect at a news conference at 11 a.m. Tuesday.
Firefighters found Chere Osmanhodzic's body in her apartment on the 11500 block of West Riverside Drive on July 24. Investigators said the fire was set to cover up her murder.
Osmanhodzic was to be married a few months from the date of her murder.
The victim's fiancé, Adam Culvey, told investigators that he had returned from the store and confronted a man inside the apartment. He chased the man several blocks but the suspect got away.
When Culvey returned, he said the apartment was on fire.
Police released surveillance video and a composite sketch of a man that matches Culvey's description of the suspect.
Madonna McGee lives down the street from the murder scene. She's said she is relieved to learn that police are ready to name their suspect in the murder.
"I was wondering why we hadn't heard anything, if they were still pursuing it," McGee said. "There's been nothing, and I've looked on the Internet and there's nothing there."
"All of us were really concerned," said Lauren Olsen, another neighbor. "I am comforted that it's coming to an end."
The LAPD posted a $50,000 reward for information leading to the suspect's arrest.
They have not said what led them to this break in the case.