The Scottish Prison Service is to hire property consultants to find potential sites for a replacement to HMP Barlinnie which was described as grossly overcrowded in a critical report in 2011.
HM Inspectorate of Prisons, which described many areas of the Victorian prison as woefully out-of-date, recommended that its future was reviewed.
A specification list on a tendering document made available to companies interested in the contract states that potential sites for a prison, called HMP Glasgow, would have to be between 200,000 and 300,000 square metres in size, far larger than the 134,000 square metre area of north east Glasgow where Barlinnie, built between 1882 and 1897, is now.
It is acknowledged that finding locations that meet the criteria within the boundaries of Glasgow "is not guaranteed", meaning the new jail could be built in the North Lanarkshire, South Lanarkshire, Refrewshire or East Renfrewshire council areas.
The Scottish Prison Service said it had previously committed to replacing HMP Barlinnie and that the project remained at a "very early stage".
However, Labour MSP Paul Martin, whose Glasgow Provan constituency includes the jail, accused the service of behaving in a secretive manner over the plan and questioned how building an expanded prison was compatible with the Scottish Government's aim of reducing the prison population.
He said: "As the local MSP, my concern is that there has been no liaison with the local community. I have never seen anything about a possible relocation to Renfrewshire. There has been no discussion of how the existing facility could be modified or any future development on site. If they move out, what do you do with a building like that?
"It's integrated into the local community, people have accepted it's there and it's a local employer. But if you're talking about a new build, people are not going to want it next door.
"Unfortunately, this is the way the prison service has worked. There have been a lot of occasions where they've taken a very insular approach. This is another example and it's extremely disappointing. I would call on them to go public with their proposals so a meaningful dialogue can take place."
It is understood that while the capacity of the new jail has not yet been set, it is planned that it will comfortably hold significantly more convicts than are in Barlinnie currently. During the 2011 inspection the prison, designed to hold 1000 prisoners, was home to almost 1500. On Friday, 1347 prisoners were being held there.
The firm that wins the tender will identify a minimum of three sites that could accommodate the replacement prison, before carrying out detailed investigations of the land and surrounding infrastructure. It may then be asked to drive through a planning application and negotiate purchase of the land.
A Scottish Prison Service spokeswoman said: "We have previously made a commitment to replace HMP Barlinnie as part of our estates development strategy. The project remains at a very early stage, but this contract is an attempt to identify a suitable site for the HMP Glasgow development."