Police were called to a ground floor flat on Falkner Street shortly before 19:30 BST.
A 30-year-old man was detained before being taken to hospital after falling ill.
Merseyside Police believe the incident is domestic related. They are not looking for anyone else.
The force added that a post mortem examination will be carried out to establish the causes of death.
As a precaution, and on advice from Merseyside Fire & Rescue Service following a report of a fuel leak inside the property, buildings on Falkner Street were evacuated.
Residents have been allowed back into their properties, with the exception of the properties either side of the address.
Detectives are appealing for anyone who may have information to contact them.
A man has been arrested on suspicion of murder after the bodies of a woman and two children were found at a flat in the Toxteth area of Liverpool.