While Victorian Health Minister Martin Foley insists Enterprize Park off Flinders Street is not planned to be the location, he says the process to choose a site is still under way.

"So nothing is ruled in and nothing is ruled out," he told the ABC.

"I can say there are no plans to place the second trial at Enterprize Park."

A report in the Herald Sun on Monday said the site now was expected to be at the southern end of the city on Flinders Street, west of Swanston Street.

It was originally to be set up near the Queen Victoria Market on the CBD's northern fringe.

Tony Doherty, the owner of Doherty's Gym on Flinders Street, slammed the idea.

"It's a terrible place for it ... I can't think of a worse spot," he said.

But Ben Vasiliou, the chief executive of the youth projects charity, said there was overwhelming evidence that a safe injecting room was needed and having it at the southern end of Flinders Street made sense.

"But no one wants it in their backyard," he told the ABC.

"What we can do this time around is make sure every agency, every support system, is in place to make sure people get the support that they need."

Labor MP Gabrielle Williams echoed Mr Foley's comments that there are "currently no plans" for a site at Enterprize Park.

But she added the need for an injecting facility in the CBD was clear.

"It's always important to focus on the recommendations around why the City of Melbourne has been identified as an appropriate site for a medically supervised injection facility, and that is around the prevalence of drug use and more than that, the impact of that drug use," she said.

"There is about a heroin death a month in that area."

State opposition leader Michael O'Brien said it would be "madness" to set up an injecting room in the CBD when the current centre in North Richmond is not operating properly.

"Why would you take that same flawed model to Melbourne CBD? The heart of Melbourne is struggling enough as it is," he said.

Last week, Victorian crossbench MP Fiona Patten advocated safe injecting rooms for St Kilda, Footscray and Dandenong, as well as the proposed site and the current location.

But Acting Premier James Merlino said the government did not support expanding the program beyond a second site.

The location of the second room is subject to a consultation process being run by former police commissioner Ken Lay.

The supervised injecting centre at North Richmond, which opened in 2018, has been controversial due to its proximity to a school.

But Mr Merlino insists the North Richmond centre is saving lives and other initial problems have improved.

Australian Associated Press