It is believed that the woman, 22-year-old Sharon Lester, had been dead for more than two days when her mother found her body. She had been beaten and repeatedly stabbed.
Merseyside police issued an urgent appeal for information about the whereabouts of Ms Lester's daughter, Jade. It is thought she was last seen nine days ago, a week before Ms Lester's body was found at her home in the Kensington area of the city.
Detectives have launched a nationwide hunt for Jade. They said it was now "critical" they found the toddler's father, who is believed to be from the area but lives elsewhere.
Yesterday Merseyside police officers were interviewing Ms Lester's boyfriend, John Park, who comes from the Tue Brook area of Liverpool. They had appealed for him to come forward in the hope that the girl may have been with him.
Detective Superintendent Russ Walsh, the officer in charge of the investigation, said: "We just do not know where she is. We would like to think she is safe and well with somebody who is taking good care of the little girl, wherever that may be. But at this moment in time we just haven't got a clue."
Police are particularly keen to speak to two men seen with a van at the house on Saturday, about two hours before Ms Lester's body was found. A police spokesman said: "They may be unconnected, but we are looking for more sightings of the van and for the man or men to come forward and tell us what they were doing there."
Ms Lester's body was found in a downstairs room at the back of the house, police said. Officers were unable to confirm whether anything had been stolen. A police spokeswoman told The Independent: "We are trying to establish if any of the little girl's clothes are missing, but obviously it is a very difficult time for the family."
House-to-house inquiries were being extended last night as forensic scientists searched for clues at the murder scene. Relatives, friends and health workers who have come into contact with Jade are being traced, the spokeswoman said. Neighbours were also being asked to come forward with any information that might help to trace the missing child.