Citing law enforcement sources, the Los Angeles Times reported Thursday the victims -- described as two men and a woman in their 50s -- survived the assaults.
Police said a typed "death warrant" was left near the scene where a 56-year-old man was stabbed July 4 with what was described as a "hunting-type" knife. There was no word on the note's contents.
A second homeless man was stabbed Tuesday as he slept on a bus bench in Santa Monica, and police confirmed a similar note was found nearby, the newspaper said.
The third such incident occurred Thursday, when a 54-year-old woman was stabbed as she slept at an intersection in Hollywood. Police said a kitchen knife was found in her back and a "death warrant" was found nearby.
Police said they were looking for a suspect -- identified as David Ben Keyes -- and said he had been missing for weeks from the Santa Barbara area.