The discovery was made in a flat in Clune Park Street on Thursday, July 31.
The 21-year-old, of Wallace Street, Port Glasgow, was last seen by a family member at her home on Thursday, July 17.
It was reported previously that there had been a number of sightings of her in the local area.
But there was no further sightings of her since Saturday, July 19.
Police confirmed following a post mortem, the death is still being treated as suspicious, pending further enquiries.