There has been intense media and public interest in the case, and much anger at the news of their release.
The Manchester Evening News has been in talks with the Attorney General after it published information on the whereabouts of Robert Thompson and Jon Venables.
But there is support for the newspaper on Merseyside where James' mother Denise joined a small demonstration by truck-drivers on Saturday
Police said five trucks festooned with protest banners passed by the cemetery where the murdered toddler is buried before heading for Liverpool city centre.
Revenge attacks
A strict injunction is in place banning the release of any details about the boys, both now 18, that is likely to lead to their identification.
The move is aimed at preventing any possible revenge attacks.
In a statement on Friday the Home Office said: "The Attorney General is considering as a matter of urgency whether it would be appropriate to issue proceedings for contempt in light of this."
Lord Goldsmith's preliminary decision on the article in the Manchester Evening News could be announced as early as Monday.
Under the Contempt of Court Act, if proceedings go ahead the newspaper could face an unlimited fine and its editor could be jailed.
Internet test
Venables and Thompson were only 10 when they abducted two-year-old James from a Liverpool shopping centre before torturing and killing him.
There has been intense media and public interest in the case, and much anger at the news of their release.
Many legal observers are seeing the Manchester Evening News case as a "test" of the authorities' determination to protect the boys.
The injunction applies only to England and Wales - it does not cover Scotland or the foreign press.
BBC correspondent Nick Thatcher said: "Anyone can publish these sorts of details about the whereabouts, about the identities of these two young men on the internet in another country.
"They could be identified and recognised here by people viewing the internet in this country."
Internet and media lawyer Mark Stephens said: "The problem that this case has always presented is 'jigsaw identification', the idea that confidential information evaporates because of each little piece of information that is published."
The case could prove to be a major test for the way such court rulings were dealt with by internet publishers, he said.
"For the first time the judiciary have had their ingenuity pitted against the entire internet community."
Life licences
Venables and Thompson, who have spent eight years in custody, are being released on life licences.
This means they will be under close observation by probation officers and subject to recall to prison in the event of wrongdoing.
But the desire for retribution in the local community is said to be running high.
BBC Radio Merseyside received a call on Friday night suggesting "terrible things should be done".
And James's mother, Denise Fergus, said the murderers should not think they would remain anonymous indefinitely.
"I know that no matter where they are, someone out there is waiting. There will be no stone unturned," she said.
It is unclear whether the pair have yet been released but it is thought likely they will both be free by the end of the month.