The official would not elaborate on when detectives think the boy died.
Police spokeswoman Monique Bond said she could not comment about the official's statements.
The bodies of the singer and Oscar-winning actress' mother, 57-year-old Darnell Donerson, and brother, 29-year-old Jason Hudson, were found Oct. 24 inside their home on Chicago's South Side. Julian's body was discovered Monday in the SUV on the city's West Side. All three had been shot.
Nobody has been charged, but the estranged husband of Julian's mother remained in custody on a parole violation. Police have characterized 27-year-old William Balfour, a convicted felon, as a "person of interest," but the official said he was the only suspect in the slayings.
Balfour, who is Julian's stepfather, had refused to take a lie-detector test and has stopped cooperating with detectives, the official said Wednesday.
It was unclear whether Balfour had an attorney.
Police Superintendent Jody Weis said Thursday that a gun found a day earlier in a vacant lot around the corner from where the SUV had been parked was a .45-caliber weapon. It was sent to Illinois State Police for testing.
Weis said preliminary tests suggest the weapon used was a .45-caliber gun, but tests should determine whether the gun found in the lot was the one used. It will be compared with shell casings found at the Hudson home, he said.
Meanwhile, a funeral home announced Thursday that services for Hudson's mother, brother and nephew will be held Monday morning.
The service at Apostolic Church of God on Chicago's South Side will be closed to the public.