The baby girl, who is thought to be between two and three weeks old and weighed around 7lbs, was discovered wearing warm clothing and a nappy inside a holdall left lying on the doorstep of a priest's house, next door to the Polish Centre in London Road, at 8.59pm.
A note written in Polish and left with the well-fed baby, asking for her to be "cared for in due course", gave the little girl's name but police refuse to reveal what it is and Reading area commander Supt Stuart Greenfield said: "Out of respect for the future carers we'd rather not release the name at the moment. The name is a certainly a line of inquiry we're following."
The baby's crying alerted a priest in the presbytery for the Polish Church of the Sacred Heart in Watlington Street, and he found the 'Globtroter' brand holdall on the doorstep.
The tiny girl was immediately taken to the nearby Royal Berkshire Hospital where she was looked after by nurses in the paediatric unit until being handed over by social workers to a foster family this afternoon.
Detective Inspector Mark Tucker, from the protecting young children unit, told a press conference this afternoon: "Our first concern is the welfare of the child, she hasn't come to any harm and is safe and well now.
"Our primary concern now is the welfare of the mother. Clearly we would appeal for the mother to come forward in case there are any welfare issues of her own and if there are any children to be concerned about from the same family."
Gill Valentine, director of midwifery at the Royal Berks, said the child had been "well cared for" and she wanted the mother to know her baby is fine and well.
Supt Greenfield said officers will be circulating flyers in Polish and English in a bid to trace the mother and added: "We're appealing for any information, no matter how insignificant that might seem, which might help us identify the mother and get the wheels in motion in terms of her own welfare. Our investigation is centred very much on locating mum and ensuring that she is safe and well."
He added: "Although we cannot say for certain that one or both of her parents are Polish, the fact that the note was written in Polish leads us to think that this may be the case. Therefore, we would be particularly keen to hear from anyone within the Polish community in Reading who may have any information relating to the baby or her mother."
Anyone with information should contact Det Insp Tucker via the 24-hour Police Inquiry Centre on 101 or Crimestoppers anonymously on 0800 555 111.