It is believed that the tanks would be similar to holding cells but with safeguards to protect detainees' health.
The tanks could be modelled on overseas "bed-and-bucket" facilities and security cameras, allowing drunks to be treated and closely monitored.
Police Minister Bob Cameron has confirmed that the issue was raised this week.
"We've had some preliminary discussions with police about the concept," the Herald Sun quoted his spokeswoman as saying.
According to reports, those arrested for being drunk would be held in the tank until they were deemed to be no threat to themselves or the public.
There is yet no clue as to how the tanks would work, and where they would be located.
However, a spokeswoman said: "Victoria Police is constantly considering options to combat public drunkenness and disorderly behaviour."
While police have yet to make a formal submission, Melbourne's CBD or regional centres like Geelong and Ballarat are being seen as the most likely candidates for the first drunk tanks.
Shadow police spokesman Andrew McIntosh fears that drunk tanks may add to the police workload without dealing with the issue of public drunkenness.
"I'd like to know what these things look like and where they are going to locate them," he said.
The discussion with the Government follows the May agreement by police commissioners on a range of measures to deal with drunkenness.
The commissioners said at the time that sobering-up centres should be used as an alternative to filling up police cells.