The Home Secretary and his officials are said to be concerned that when the two boys - Jon Venables and Robert Thompson - 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 confirmed that a working group set up to examine the issues raised by the Cries Unheard episode had now reported, and ministers were considering its recommendations.
But she said no final decisions had been made, describing as "speculation" the suggestion that the review had recommended new legislation.
Last Thursday, the European Court of Human Rights in Strasbourg ruled that the two young killers of James Bulger did not receive a fair trial.
The finding that the boys' trial in an adult courtroom amounted to a breach of their human rights is expected to force the Government to change the way juveniles are tried and sentenced for serious offences.
The court also ruled that a decision by Michael Howard, then Home Secretary, to set a minimum term of 15 years for the 1993 murder of the two-year- old in Liverpool was a violation of the European Convention of Human Rights.
It awarded both boys costs against the Government, which will have to pay pounds 29,000 to Venables and pounds 15,000 to Thompson.
Mr Straw accepted the judgment which is likely to lead to the release much earlier than expected of Thompson and Venables - possibly in 2003.Reuse content