A safe drug-injecting room for Melbourne will be considered by the Andrews government after a spate of overdose deaths.

Political support for the controversial idea is gathering pace amid concern that the government's tough-on-crime approach has taken the focus off harm minimisation.

Credit:Jason South

An inquiry by Coroner Jacqui Hawkins into the death of a 33-year-old woman in north Richmond is expected to recommend a safe drug-consumption room.

The government will also consider new laws introduced to state parliament by Sex Party MP Fiona Patten to establish a drug room so users could be supervised by medical professionals and given access to social work and mental health services.