Members of the health board, city council and police agreed the proposals in principle but called for more details on the cost, where the clinic would be, and how it would operate.
The plan would see a facility made available for addicts to consume their own drugs.
In some cases users would be provided with medical-grade heroin.
The move aims to address the problems caused by an estimated 500 or so users who inject on Glasgow's streets.
Such a facility would be the first of its kind in the UK.
The group also advised that a safer injecting facility should also provide the means for the supervised inhalation of drugs.
The case for opening an injecting facility for drug users in the city was examined by the Glasgow City Alcohol and Drug Partnership (ADP) - a multi-agency group tasked by the Scottish government with tackling alcohol and drug issues.
It also says street users experience problems such as homelessness, mental health issues and poverty, and are at heightened risk of blood-borne viruses, overdose and drug-related death, as well as other injecting-related complications.
The Scottish Drugs Forum (SDF), a drugs policy and information organisation, has estimated there about 90 similar injecting facilities operating around the world, most of them in Europe.
Recently a Paris hospital started housing France's first "shooting gallery" - a safe place where drug addicts can inject under medical supervision.
The drug room was opened by the Paris mayor and health minister near the Gare du Nord, a busy station where drug crime is common.
More than 3,900 discarded needles were reported in nine of Scotland's largest towns and cities over two years.
The figure was revealed by a series of freedom of information requests to the local authorities covering Aberdeen, Cumbernauld, East Kilbride, Dundee, Edinburgh, Glasgow, Hamilton, Kirkcaldy, Livingston, and Paisley.
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