Another relative found the slain family members, who lived in Epping in the northwestern suburbs, The Daily Telegraph reported. They were identified as Min Lin, 46, Lilly Lin, 44, their sons, Henry, 12, and Terry, 9, and a 40-year-old woman whose name was not released.
Brenda Lin, 15, a daughter, was in China visiting her grandparents.
Lin ran a newspaper store, which he opened several years ago. He told an interviewer in January he wanted to own his own business even though he was a trained engineer.
Police said they were trying to determine whether the family might have been killed because Lin saw the robbery of an armored car across the street from his store May 27.
"It's going to be a long, protracted inquiry," said Stephen Henkel, acting superintendent of the Eastwood Police.