Jack Straw, the Home Secretary, will outline plans to create a new system of detention of those individuals who currently fall outside the remit of the prison service and NHS.
The move follows ministers' concern over the case of Michael Stone, the psychologically disturbed man convicted of murdering Lin Russell and her daughter Megan.
Mr Stone asked to be admitted to a psychiatric unit before the killings, but was refused by doctors.
In a statement to the House of Commons, Mr Straw will announce that police and social workers will be able to apply to magistrates to have a person assessed if there are reasonable grounds to believe they pose a danger to society.
The proposals will allow for people to be detained even if they have not been convicted of a violent offence - a suggestion likely to provoke opposition from civil liberties groups.
The "third service" detention centres will offer counselling and therapy, but the Government is determined to ensure those who have untreatable disorders do not roam the streets.
People with non-treatable personality disorders slip through the net between hospital, where they can only be detained if deemed "treatable", and prison, where they can only be held for the duration of their sentence.
The problem was highlighted by the case of Stone and paedophiles such as Robert Oliver, who had to be released from jail even though he was considered a public danger.
Up to 2,700 people deemed to be "walking time bombs" are expected to fall within the remit of the new system.
Civil liberty campaigners said that such individuals needed to be dealt with more effectively, but the Government's proposals were "deeply problematic" and could cost up to pounds 40,000 a year per person.Reuse content