The naked body of Christine Askey, 20, was discovered by her mother in the home she shared with her three-year-old son Cameron in Preston, Lancashire.
Police are yet to question the child, who may have vital clues to the identity of the killer. Police also want to trace the father of the unborn child, as detectives believe he is a potential suspect.
Miss Askey was single and had her first child with a different man.
Her body was found on Monday morning by her mother, Pauline Coombes, who lives opposite her daughter in Nevitt Street, on the Callon estate.
Cameron was running around the house when Mrs Coombes went to check on her daughter, who was last seen alive at 8pm on Sunday. She discovered her daughter's body face down in the bath, which was a third full of water.
Forensic experts are trying to establish whether Miss Askey was strangled in the bath or whether her body was placed there after she died. She was described as devoted to her son and was not known to visit local pubs and clubs.
Detective Superintendent Paul Buschini, who is leading the investigation, said trained officers would interview the dead woman's son over the next few days.
A spokeswoman for the Lancashire Constabulary said she was unable to confirm reports that Miss Askey was pregnant, but said detectives were awaiting the findings of the pathologists.
Sheana Warren, a neighbour of Miss Askey's mother, who was looking after Cameron, said he was "bearing up very well". "Christine was a great mum, absolutely devoted," she added.Reuse content