The Vatican has invited a homeless woman to stay after she gave birth on a piece of cardboard near St Peter's Square, according to The Washington Post.

The woman is said to be considering the offer after Italian police stopped to help her as she gave birth just outside Vatican territory at 2am on Wednesday morning. Temperatures were near freezing at the time.

"When I got close I saw that the baby was already born and was still attached by the umbilical cord to the mother," one of the responding officers, Maria Capone, told the Associated Press.

"With my colleagues we tried to warm them up. We covered them with our uniform jackets."

Pope Francis' Papal Almoner knew the baby's mother and father, who are both Romanian, as they sometimes showered at facilities his office had built for the homeless.

Monsignor Konrad Krajewski visited the mother and baby at a nearby hospital and offered them a place to stay.

She is yet to decide whether to accept, according to Vatican spokesperson Rev Federico Lombardi.

Francis has become known for his focus on the poor and the homeless. A new shelter on the outskirts of St Peter's Square was opened last year and within days Francis visited the centre to spend time with and speak to inhabitants.

On his tour of the US last year, he famously declined an invite for lunch with politicans in favour of a meal with local homeless people.