Using CCTV footage, and phone triangulation, the police have placed the suspect in the Ruaka area, Kiambu County where he seems to have been staying for days.
The team visited the area Monday and asked for footage of surveillance cameras on several buildings as part of the probe.
This will enable them to identify the suspect whose image was captured outside the apartment where he murdered the woman.
The woman's(whose identity has not been made public) family visited City Mortuary, Nairobi on Monday and identified her.
However, because key body parts were missing, they were asked to wait for further analysis of the samples collected from the body and close relatives before they made public any information on her.
The motive of the incident remains unknown, police said adding the suspect dismembered the woman’s body severing the limbs, arms, and head from the torso.
He then wrapped the body parts in a bedsheet and paper bag.
There were marks of the hacksaw on the body when police arrived to pick it up at the mortuary.
It also emerged the man had called to book the room using a mobile number registered under a woman’s name.
What we know about the dismembered bodies found in Kware