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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Showers gradually fading away this evening, leaving a largely dry, clear and chilly night, with some patchy fog and frost forming.
Showers soon dying out this evening to give a dry night with some long clear spells and light winds.