Venables and Robert Thompson were aged 10 when they were convicted of killing the toddler in 1993.
In 2001, when the pair were released on licence aged 18, the High Court judge banned publication of any information which could lead to the revelation of their new identities.
They are protected by an injunction granting them lifelong anonymity.
The image, which was uploaded to the micro-blogging site on Tuesday, was claimed to show Venables as a adult at a birthday party with friends.
The originals have now been removed from Twitter, but there is concern that more have been posted elsewhere online.
“The AGO has been alerted to a possible contempt of court. We are liaising with the MoJ (Ministry of Justice) and others to establish the facts,” a spokesman for the Attorney General’s office said.
”We can neither confirm nor deny whether the pictures in question are of Jon Venables. It should be noted, there is a worldwide injunction in place which prevents the publication of any images or information purporting to identify anyone as Jon Venables.”
Venables, 30, had his parole revoked in 2010 and was jailed for two years after admitting downloading and distributing indecent images of children but is expected to make a fresh application for release in the coming months.
It is believed the image on Twitter could have been seen by thousands of users. The user who posted the image wrote: “Obviously no one can officially confirm it, [but] the pics are clearly him and while drunk he himself told people his real identity.”
Venables and Thompson abducted James Bulger from a shopping centre in Liverpool before torturing him and leaving him for dead on railway tracks.
Image via Getty