Ralph and Jimmy Bulger are challenging a worldwide ban, made in 2001, on revealing the identity of Venables.
Venables has been living anonymously since his release from a life sentence for the kidnap, torture and murder of two-year-old James in February 1993.
The toddler was killed by Venables and Robert Thompson, both aged 10, after they snatched him from a shopping centre in Bootle, Merseyside.
They were both later granted lifelong anonymity and, following release, have lived under new identities.
James’s mother, Denise Fergus, is not involved in the proceedings and no challenge is being brought against the anonymity granted to Thompson.
The court order was amended in relation to Venables after he was convicted of further offences in 2010 and February last year.
Solicitor-advocate Robin Makin, for the Bulgers, has said that the injunction was granted on the basis that Venables was rehabilitated and would not re-offend but he had since been convicted and sent back to jail over indecent images of children.
In written submissions previously before the court, Mr Makin said: “The applicants consider that over 17 years on and with serious offending the experiment of ‘anonymising’ Jon Venables has not worked and that there is danger in seeking to continue with such a course.”
The case is being heard in London on Tuesday and Wednesday by the President of the Family Division, Sir Andrew McFarlane.
In a ruling on preliminary issues in May last year, then President of the Family Division Sir James Munby said the murder of James Bulger had “shocked and horrified the country”.
Only a handful of lifelong anonymity orders have been made to date, including those granted to Jon Venables and Robert Thompson, who murdered Liverpool toddler James Bulger, and child killer Mary Bell.