The body of the woman was found in a flat in West Princes Street, Woodlands around 4pm on Monday, June 1.
Police have launched an extensive investigation to establish the circumstances around the death and a post mortem will be carried out in due course.
Detective Superintendent Suzie Chow, of Police Scotland’s Major Investigation Teams and senior investigating officer said: "Whilst we are at the early stages of the investigation into this suspicious death, we are following up a number of lines of enquiry and I would ask anyone who has any
information that could assist with our investigation to please get in touch.
"It is imperative that we trace whoever is responsible for this woman's death as soon as possible.
"The area of West Princes Street is very residential and we are sure that there will be people who may have witnessed something untoward in the lead up to the discovery of the woman's body yesterday.
"If you have any information, no matter how insignificant it might seem to you, please contact us as soon as possible."
Detectives are working closely with local uniformed police officers and lines of enquiry are already underway to formally identify the woman.
Superintendent Ross Allan of Greater Glasgow Police Division, added: "This is a very distressing incident and we understand that the local community will be extremely shocked and concerned about this, but I would like to take this opportunity to reassure them that we have a team of officers
working alongside our detective colleagues to trace whoever is responsible for this crime.
"Additional officers will be in and around the local community of Woodlands and I would encourage anyone with any concerns or any information to approach these officers."
Detectives have set up an online portal to encourage members of the public to submit information which can be accessed here.
Anyone with any information can also contact police via 101 quoting reference number 2559 of Tuesday, 1 June.
Crimestoppers can also be contacted anonymously on 0800 555111.