West Midlands Police have received around 150 calls from members of the public, offering information and suggestion names of people that could possibly by the baby's mother.
The baby, named Jade by hospital staff, was found abandoned in a carrier bag in a park in Stechford, Birmingham, last month.
The girl is thought to have only been one or two days old when she was abandoned.
A spokesperson for the force says all the calls are being considered by the team investigating.
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Paramedics had to take the boy to a hospital 18 miles away from his home following the closure of a local children's A&E.