The idea is part of an urgent review of the scheme following local authorities' failure to take out the orders since they came into operation in 1998.
Under the scheme, councils can apply to impose a curfew banning children under 10 from specified places between 9pm and 6am.
Mr Straw is now considering whether the upper age limit for curfews should be increased from 10 to 14 years in an attempt to encourage councils to make use of the powers in the Crime and Disorder Act.
Such orders can be issued by magistrates when they fear a child under 10 is at risk of becoming involved in crime. The child will be required to be under the supervision of a council official.