The proposed unit would house around 76 patients, many of whom are convicted rapists and paedophiles.
The plan is being opposed by local residents who do not want patients with criminal convictions based near their homes.
They are being backed in their fight by medical staff from Stobhill Hospital who feel the views of local people should come first.
The proposed unit would house around 76 patients, many of whom are convicted rapists and paedophiles.
The man in charge of the consultation exercise says he has an open mind and will be happy to discuss alternative sites for the unit with members of the public.
Professor Alan Alexander said: "There are community council representatives from the immediate area and there are professionals from the various disciplines involved from the medical profession.
"My job is to make sure that everybody's voice is heard."
Serious misgivings
But local people fear the consultation may be a public relations exercise and the unit will be based in Stobhill whatever their concerns.
Resident Karleen Collins said she has serious misgivings about the plan.
"We just feel that if this secure unit is built in this site, we'll have a hospital on our doorstep that we can't use," she said.
Greater Glasgow Health Board will also hear the objections of medical staff from Stobhill duribg the two days of consultation.
Dr. Fiona Johnston said: "It seems to be that the population of the north district of Glasgow, 200,000 people's needs are being by-passed for a unit of 72 individuals from the whole of Glasgow.
"I do think that the population of the north of Glasgow has primacy over these needs."
The consultation exercise was forced on Greater Glasgow Health Board last year after an intervention by the Scottish Parliament's health committee.
The board has promised to consider other possible sites for the secure unit as part of the consultation.