The victim is thought to have been dead inside the property for as long as three weeks, the time when she was last seen by friends.
Police Scotland's major investigation team are carrying out door to door inquiries and speaking to the woman's neighbours.
Her body was found on Wednesday at a flat in Dobbies Loan Place in the Townhead area of Glasgow.
Officers forced their way in and found the body inside.
CCTV is also being examined from the estate as officers seek clues to the identity of her killer.
Police are describing the attack as unprovoked and are investigating for a possible motive.
However, sources said yesterday that despite the length of time between her disappearance and discovery of the body the inquiry is "progressing well".
Police have revealed the woman was seen on Wednesday October 9 and they are keen to establish her movements. Detective Chief Inspector Colin Carey said: "We are trying to establish a motive for this attack as it appears to have been unprovoked.
"We know that the woman was seen on Wednesday 9 October 2013 and we need to establish her movements from then on, who she saw, where she went, so if anyone has any information please do get in touch with us."
Meanwhile, detectives are continuing their inquiries after the body of a 40-year-old woman was discovered at an address in Forfar, Angus, on Friday morning. Police say the discovery is being treated suspicious and the property was cordoned off for forensics tests to be carried out.
A spokesman said inquiries underway to establish the full circumstances of the incident.
The identity of the dead woman has not been named, but she is said to be Catherine Sandeman.
A 33-year-old man has been arrested and will appear at Forfar Sheriff Court today in connection with the incident. A report will be submitted to the Procurator Fiscal in due course.