A 42-year-old Cuban national is still in police custody for the murder of Johandrys Espinosa.
Espinosa, 31, was found dead at a house in Flagstaff Hill, Long Circular Road, St James, last Thursday night.
Police said the man, who reportedly admitted to strangling Espinosa, has not yet been charged and is expected to be interviewed by investigators.
Police said after arrest, someone can be held between 48 and 72 hours, but they can hold a suspect for up to two weeks if granted permission by a judge.
St James police responded to reports of a domestic disturbance at the house at around 7.40 pm last Thursday.
The man answered the door and told police Espinosa was sleeping. Police insisted on seeing Espinosa to make sure she was safe, and were taken to the bedroom, where she was found unresponsive. A district medical officer was called in and declared her dead.
Investigators from the Homicide Bureau of Investigations Region 1 are continuing enquiries.