Police have confirmed their major incident team will inquire into the circumstances surrounding her departure.
Officers are appealing for any information members of the public might have in helping them with their own enquiries.
A post-mortem is going to be completed so as to ascertain the circumstances surrounding the lady's passing which cops are currently treating as suspicious.
Detective Superintendent Suzie Chow, of Police Scotland's Major Investigation Teams and senior investigating officer stated:"Whilst we're in the first phases of the investigation to this questionable death, we're following a number of lines of enquiry and I'd ask anybody with some information that could help with our analysis to get in contact with It's very important that we trace whoever is in charge of the lady's death when possible.
"The region of West Princes Street is quite residential and we're certain that there'll be individuals who might have seen something untoward in the lead up to the discovery of this female's body . In case you have any advice, however insignificant it may seem to you, please contact us as soon as you can."
Superintendent Ross Allan of this Greater Glasgow Police Division verified that extra police patrols are going to be in the place.
