Firefighters were called to the two-story structure in East Compton shortly after 2 a.m. and found the auto repair shop and loft fully engulfed in flames. The father and two other children had escaped the blaze but the woman and child were still inside, Los Angeles County Fire Inspector Scott Miller said.
The Los Angeles Times reported Miller described the interior of the loft as "pack rat-like," with heavy content that caused the fire to burn hotter and longer than it otherwise would have.
The family lived above the car shop the father managed, the Times said.
Firefighters attempted to stage a search and rescue operation inside the loft but it was deemed too risky. A short time later, the second floor collapsed. Miller said cadaver dogs were brought in to survey the scene once the fire was extinguished.
As of Monday morning, firefighters had yet to recover the bodies.
"It's a lengthy process with the amount of debris," Miller said. "But we are taking every measure."
The fire's cause remained under investigation.