The Attorney General is investigating a possible breach of the law after one of the killers of James Bulger was reportedly identified on social media.
Venables - who was recently sent back to prison after images of child porn were found on his computer - is subject to a lifetime order of anonymity.
The ruling, granted in 2001 shortly before his release from prison, makes it illegal to identify Venables and his fellow killer Robert Thompson or reveal their current identities.
The office of Jeremy Wright, the Attorney General, has said it received reports of a breach of an anonymity order and was currently investigating.
The father of James Bulger, Ralph, recently called for Venables' anonymity to be stripped in light of his recent arrest and return to prison.
The 51-year-old blasted a decision to spend £5 million on rehabilitating both Venables and Thompson.