The 28-year-old's torso was found inside a duffel bag on the trail near Jane Street and Alliance Avenue on May 24. Police said she had last been seen a week and a half earlier on May 15.
A permanent resident of Canada, Ghirmay moved here in 2009 from Eritrea, located in the Horn of Africa.
Toronto police Det. John Margetson said on Monday that investigators had been in contact with the woman's family, but were still hoping to speak with anyone who "could assist us in her movements in the last several weeks, as well as any acquaintances she may have had in the Toronto area."
Police also released a photo of the green and black Tracker duffel bag involved in the investigation.
Margetson said homicide investigators are hoping to speak with witnesses who may have seen the bag being moved in the area of Humber Boulevard and Alliance Avenue in the last two weeks.
The only arrest in the case has been 41-year-old Adonay Zekarias, who was arrested two days after the remains were discovered and charged with committing an indignity to a dead body.
Margetson said there was a "high likelihood that the charges will be upgraded to murder" and that evidence collected suggested that Zeharias had acted alone.
Police have only been able to find one-third of Ghirmay's body, even after searching sections along the Humber River and waste transfer stations.
Margetson said the Ghirmay's cause of death has not been determined by the coroner.
There is conflicting information on how Zekarias and Ghirmay came to know each other.
Margetson said the two had "frequented" places and even lived together at one point in the past.
"We're not sure exactly how they met up or if their relationship continued," said Margetson.
Police said they haven't been able to confirm initial reports suggesting the pair had taken an English as a Second Language class, as well as a cooking class.
Margetson said investigators haven't been able to locate any friends or acquaintances of Zekarias and are asking anyone with information to come forward.