The Home Secretary and his officials are said to be concerned that when the two boys turn 18 next year, and tight restrictions on reporting their progress are lifted, there will be a wave of publishing offers.
Under the present law, criminals are prevented from receiving payments for their story for six years. Mr Straw is considering extending that ban, both for criminals and their families, to life.
The new rules would not prevent them from talking or writing about what they did, provided they did not receive payment.
Mr Straw ordered a review of the law last year after the publication of Cries Unheard, a book by Gitta Sereny about the child killer Mary Bell, who was paid pounds 10,000 for her help.
Under the Proceeds of Crime Act 1995, an application can be made to the courts to grant a confiscation order within six years of a crime. The legislation was designed to recover the proceeds of organised crime and, in any case, would not cover the Bulger murder, which happened seven years ago.
A Home Office spokeswoman said that a working group to examine the issues raised by the Cries Unheard episode had now reported and that ministers were considering its recommendations.