Ministers are looking at the "options available" for dealing with bad behaviour by young children, Transport Secretary Alistair Darling has said.
Sanctions would be 'lighter' than for over-10s, reports say
Children's charity the NSPCC said media reports of some of the government's proposals, such as segregating problem families, were "deeply disturbing".
The Sunday Telegraph said anti-social behaviour orders for under-10s may be created, which the NSPCC also slammed.
A Downing Street spokesman said he did not "recognise" the plans reported.
But Mr Darling told ITV1's Jonathan Dimbleby show ministers had to "deal with" very young offenders who made people's lives a "misery".
Currently under-10s cannot receive Asbos because, under law, they are not considered capable of committing a crime.
The Sunday Telegraph said adapting the orders to this age group would involve a "lighter sanction" and that younger children were "unlikely" to be named and shamed.
Asbos prevent those affected from committing specified anti-social acts or entering certain areas.
Mr Darling said: "There are many parts of the country in many communities where a lot of problems have been caused by surprisingly young children and we have to ask ourselves how do we deal with that.
"What we're doing at the moment is looking at the options available to us, in order to ensure that people do not have their lives disrupted or sometimes made a complete misery."
Any "baby Asbo" plan is thought to be a long-term one, precluding it from being included in the government's forthcoming Respect Bill.
It is thought that this legislation will extend the system of parent orders, which force families to seek help to improve relationships and discipline.
Binge drinkers who repeatedly offend could be named and shamed in a similar way to those given Asbos, according to political commentators.
The Mail on Sunday reported that possible proposals could include "sin bin" residential units for "neighbours from hell", to be policed by security guards with powers to impose curfews and detain residents.
The paper also suggested the prime minister was looking at plans to confiscate the homes of parents whose children are accused of persistent anti-social behaviour.
A Downing Street spokesman said: "The prime minister has been very clear about making anti-social behaviour one of his priorities."
But he added: "We don't recognise these specific ideas. There is a consultation and discussions going on with police about what additional powers they need."
The NSPCC's public policy director Phillip Noyes said the measures, reported in a number of Sunday papers, would do "more harm than good" if they were introduced.
"These reported proposals are deeply disturbing," he said.
"Children who cause trouble can themselves come from very troubled backgrounds.
"Their behaviour must be addressed in a way that meets their best interests."
He added that any plans to extend Asbos to children under 10 must be approached with "extreme caution" as children under the age of criminal responsibility should not be drawn into the criminal justice system.
Shadow home secretary David Davis said: "With the legal age of criminal responsibility being 10, the government needs to explain how the breach of such an Asbo could be punished.
"There is also a serious risk of stigmatising a child of such a young age, even without naming and shaming them."
Liberal Democrat home affairs spokesman Mark Oaten said Asbos were a "quick-fix" solution to complex social problems.
He told The Politics Show on BBC One it was more important to "break the cycle" of offending.