The family's neighbors, who claimed the victims were doused with accelerants and set ablaze Saturday in the 4200-block of West 21st Place, seem to corroborate the findings.
"We believe we know who the offender is. We believe we know what happened. We are just tying some lose ends before we can make a call on it," said Police Superintendent Garry McCarthy.
The fire is believed to be the result of a domestic argument between Taniya Johnson, 30, and her live-in boyfriend.
Johnson has died as a result of the fire.
"I heard arguing downstairs. He's like, why are you doing this? And the next thing I hear is 'Mom I'm on fire!" said Tyshun Jordan, who lives upstairs.
Firefighters say they were called to the scene just after 4:30 a.m. Saturday. They saw no flames, but lots of smoke. Witnesses describe a terrible scene.
"The little boy was burned. I picked him up, got him to the police officer. I tried to help everybody, my grandmother, aunt and son, we all got out," said Tameka Johnson, who also lives upstairs.
"When I got there, there was person on the front lawn, and I saw the steam coming off of her body. I've also seen her burn marks, and they were just undescribable. It was a horrible, horrible scene," witness Ferdinand Miranda said.
According to authorities, Johnson lived in a first-floor unit of the Lawndale-area building. The other adult critically injured, a man, also lived on the first floor.
Fire officials say one of the two injured children is a 4-year-old girl who suffered 100 percent burns. The other child, a 9-year-old boy, suffered nearly 100 percent burns.
Authorities say the children were not likely to survive.
Distraught family and friends tried to console one another.
"I don't know what happened. I'm just hurting so bad," said Shelia Johnson, mother of Taniya Johnson.
An 84-year-old woman and a woman in her 50s who live on the second floor were also injured. They were hospitalized for smoke inhalation.
"It was basically a one room fire... We had smoke throughout the building," Battalion Chief James Purl said.
"First arriving battalion chief sees number of victims. He requested an EMS Plan 1, which immediately brings five additional ambulances, brought in more manpower, transported six people. Four were red. Two were yellow," said Chicago Fire Department Dist. Chief Peter Van Dorpe.
Police remained on the scene hours after the incident. The home is being considered a crime scene.
Saturday afternoon, firefighters passed out free smoke detectors as a part of their fire safety campaign as stunned neighbors struggled to cope with the tragedy.