The NHS, Glasgow City Council and Police Scotland are expected to agree to the idea in principle.
The plans, which was give users medical-grade heroin to inject under supervision, could help alleviate problems with the estimated 500 heroin users who inject on Glasgow’s streets.
According to the BBC, the proposals are due to be considered by the Glasgow City Integration Joint Board.
Similar schemes operate in 10 other countries, including Australia, Germany, France and Switzerland.
Dr Emilia Crighton, director of public health at NHS Greater Glasgow and Clyde and vice-chairwoman of the ADP, said the organisation had looked at expert evidence from around in the world.
She added: “Nowadays we see that actually that most of Europe is providing addiction services.
“There are safe consumption rooms - Switzerland has a model where there is heroin-assisted treatment and opiates-replacement treatment that satisfies the needs of the population.
“So we really have to find a solution that brings the solutions elsewhere in the world to Glasgow.”
Kirsten Horsburgh, from the Scottish Drugs Forum, said: “When we look at our rising numbers of drug-related deaths, if we are really serious about reducing the harms associated with problematic drug use then we need to be using all types of services, all evidence-based approaches to making sure that we can try and reduce the harms caused by problem drug use.
“We already provide sterile injecting equipment. Providing a sterile environment in which people can use drugs is an obvious and necessary next step.”
The initial details of the Glasgow proposals have still to be worked out, including how much the so-called fix rooms would cost, where they would be and how they would operate.