Reason Party MP Fiona Patten will call on the government to set up centres in St Kilda, Footscray and Dandenong.

"People are injecting in our streets, on our front lawns, and they are dying - we need to do something," she told AAP on Tuesday.

Along with the controversial current site in North Richmond and a second location under consideration at the Queen Victoria Market, Ms Reason's plan would take the total number of clinics in Melbourne to five.

She wants the new centres to also have the capacity to carry out pill testing.

But Acting Premier James Merlino has told reporters the government does not support expanding the program beyond a second site.

He says the expansion to Queen Victoria Market is in response to an independent review of the program released last year.

"There was a recommendation that there should be one further safe injecting room in the Melbourne CBD and that is precisely the work that we are doing.

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

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

The opposition's David Davis says the local community is increasingly angry about the centre's impact.

"The impact on local communities has been severe, it has acted as a honey pot, bringing the suppliers and the traders of these drugs into the surroundings of the school," he said on Tuesday.

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

"We're seeing less antisocial behaviour near the school and less drug paraphernalia," he said.

A review of the service released last year showed almost 120,000 visits in its first 18 months, mostly to inject heroin.

The review said staff had been able to intervene in more than 270 very serious overdoses and it's estimated they prevented between 21 and 27 deaths.

Ms Patten is in New Zealand talking to local MPs, who are currently considering safe injecting rooms.

Australian Associated Press