The hostels have been running for around 18 months with up to four suspects released on bail and tagged former prisoners with no set address.
Their exact location is not known – but three are in the Nottingham East constituency and one is in Nottingham North.
Justice officials have admitted residents are not given prior warning when the hostels are moved in to neighbourhoods.
And they say the public "should not" know when former convicts and suspects are living nearby.
At the moment the company running the hostels, ClearSprings, only has to consult police, probation services and council officials – but not councillors or residents.
Councils can only object to the sites if the housing is not fit for occupation or breaches planning legislation.
City councillor Gerry Davey, who represents Bulwell Forest, said the hostels should be discussed openly.
He said: "Elected representatives should absolutely be given prior knowledge when something like this comes into the neighbourhood.
"Politicians should prepare themselves for the uproar that follows."
Opposition MPs claimed the Government was trying to covertly introduce more hostels into neighbourhoods and that they were only needed because prisons were overcrowded.
Shadow justice secretary Nick Herbert said: "The Government has failed to provide enough prison capacity so they've devised a covert plan to set up what amounts to mini-open jails in residential areas while avoiding any consultation with the public.
"Placing offenders in residential properties causes immense aggravation when neighbours suddenly discover what's going on, only to be told that they are powerless to stop it."
Meanwhile Justice Minister David Hanson explained that no sex offenders or people that posed a threat to the public were held in the hostels.
He said that residents in the accommodation were no different to those who had been legitimately released into the community to return to their own homes.
"Those held in ClearSprings accommodation are deemed not to require close supervision or support," he said.
"More than half of those held in this accommodation are on bail and are therefore innocent until proven guilty.
"Those on Home Detention Curfew are assessed as low risk before entry, monitored during their stay, and are liable to recall to prison if they break the terms of their release."
Last year a former ClearSprings employee warned that public safety was at risk in a television news report.
But Government officials argued yesterday that the hostel locations should not be released.
A Ministry of Justice spokesman said: "If a person who is on bail or tagged returns to their home address we do not inform their neighbours.
"Similarly, when people take up residence at the hostel neighbours are not made aware."