Venables, who along with Robert Thompson tortured and killed toddler James Bulger in 1993, was arrested last week, according to The Sun.
Officials are said to have found indecent material on a computer during a routine check at his home.
The reported arrest follows an incident in 2010 when Venables was sent back to prison for downloading and distributing child pornography.
Now 35, Venables is subject to life-long licence conditions for his role in the murder of two-year-old James when he and Thompson were just 10 years old.
A source close to the investigation told The Sun: "It's all about protecting the public.
"We have these systems so those who could be a risk to the public are picked up.
"That's what happened here."
As reports emerged on Wednesday night, James's mother Denise Fergus tweeted: "Here we go again."
After serving eight-year sentences for James's murder, Venables and Thompson were granted life-long anonymity that saw them released under new identities in 2001.
Venables went on to offend again, including arrests for affray and possession of cocaine in 2008.
In 2010, he was jailed for two years after pleading guilty to downloading images of child abuse.
Venables, who was reportedly given a second new identity after his first alias was revealed, was granted parole in 2013.
In response to his latest reported offending, a Ministry of Justice spokeswoman said: "We do not comment on individuals."