A woman and a man, both in their 30s, were arrested yesterday on suspicion of child neglect, and have been released on bail.
A number of calls had led detectives to the woman.
The baby, named Joseph by hospital staff, was wrapped in a Hessian bag and left at a doorstep in Lower Wick on 18th July. The baby was only thought to be 24 hours old when he was left.
Since then, Joseph has been cared for by midwives at Worcestershire Royal Hospital, before being passed on to the care of foster parents.
More top news
A 3-year-old child grabbed his mother's gun from her purse when he went to get her iPhone, police said.
A 350,000 ton landslip in the Harbury area between Leamington Spa and Banbury yesterday is affecting both train services.
It is freezing cold again today in the cutting north-north-west winds. Northern Scotland can expect to see some snow.