She told the newspaper she believes she may have had a brief relationship with him in 2008 after he had been released from custody for the murder of toddler James.
He was known by another name at the time and she had no idea of his past when she fell pregnant.
The relationship ended before she gave birth after she discovered he was a Schedule One offender – a person who has been convicted of the worst crimes against children. But she was not aware of his true identity or the exact nature of his offences.
She cut off all contact after being warned by social services that the man was a risk to children. The mum has never heard from him since and is understood to have been advised by social workers not to put the name of the father on her child's birth certificate.
She told the Mirror: "The pictures were basically the same. Except in the pictures I had he was smaller, weight wise.
"It was a bit of a shock to me. I would never have put two and two together.
"The stories all match up, the pictures are there. What more can I say really? I knew that this person I was with was a Schedule One offender – and that was all I knew."
The woman, whose identity is being protected by the newspaper, is understood to have met the father of her child on a dating website.
She said: "I know I had a child with a Schedule One offender who is now untraceable. I haven't got a clue who he is. I have not seen him for four and a half years. He was 26 at the time.
"It could be Venables. Perhaps I am never going to know for sure."
Venables and Robert Thompson, from Liverpool, were both 10 when they abducted and murdered two-year-old James from a shopping centre in Bootle, Merseyside in 1993.
They were released on licence in 2001 and given new identities. A legal order was put in place for their lifetime banning the publication of any information about them, their new identities or their whereabouts.
Venables was jailed again for two years in July 2010 after pleading guilty to downloading and distributing child pornography.