James Bulger was murdered on Merseyside in 1993
James Bulger's mother is calling on Jon Venables' anonymity to be taken away if he is charged over the "extremely serious allegations" he faces.
Venables, now 27, was released in 2001 and given a new identity after serving eight years for the murder of two-year-old James on Merseyside.
A report in the Sunday Mirror claims Venables was returned to jail "on suspicion of child porn offences".
Denise Fergus said Venables should face any charges under his real name.
Speaking on behalf of the 42-year-old before the Mirror published its claims, spokesman Chris Johnson said Mrs Fergus was "appalled" by Venables' return to jail.
He said she believed that if Venables were charged with any offence he "ought to go before a court in his own name".
"If after that, depending on the outcome of the court case, the powers that be decide that he should have some new identity yet again, then we'll deal with that when we come to it," said Mr Johnson.
"But she can't understand why he doesn't appear in a dock under his own name, if that's going to be where he ends up."
Mr Johnson added: "She's appalled. She doesn't think that he should be at liberty anyway.
"He should really have served a sentence of something in the order of 15 years and should be coming up for parole now.
"In her mind, if there has been an offence committed, it means that that could have been avoided."
Jon Venables was released from prison under licence conditions
Justice Secretary Jack Straw's office has contacted Mrs Fergus to arrange a meeting, which she hopes will take place next week.
However, government sources have told the BBC that James's mother will not be told why Venables is back in jail.
Venables and Robert Thompson - both aged 10 - became the UK's youngest murderers after abducting James from a shopping centre in Bootle.
Ever since the news broke that Venables had breached his licence and had been returned to jail, ministers have refused to release details of his alleged offence.
James's battered body was found by children playing on a freight railway line more than two miles from the shopping centre in February 1993.
Thompson and Venables were given life sentences, but released in 2001 with new identities and under certain licence conditions.
A court order prevents details being published which could reveal their whereabouts.
A report in the Sun newspaper on Saturday claimed Venables was alleged to have committed a serious sexual offence.
BBC home affairs correspondent Danny Shaw said government solicitors had attempted to prevent the Sun publishing full details of the allegations against Venables.
On Wednesday, the Home Secretary Alan Johnson had said he believed the public "had a right to know" why Venables was back in jail.
But Mr Straw, appearing to overrule his colleague, insisted that secrecy was in the public interest - and he was later backed by the prime minister.
Denise Fergus has a lot of questions, her spokesman says
Mr Straw went further on Saturday, revealing in a statement that Venables faced "extremely serious allegations".
"I said on Wednesday that I was unable to give further details of the reasons for Jon Venables' return to custody, because it was not in the public interest to do so," said Mr Straw.
"We all feared that a premature disclosure of information would undermine the integrity of the criminal justice process, including the investigation and potential prosecution of individual(s).
"Our motivation throughout has been solely to ensure that some extremely serious allegations are properly investigated and that justice is done."