Sadly it was confirmed the baby boy, believed to be newborn, had died.
Officers from West Midlands Police said on Monday they are still trying to trace the mother of the baby so they can get her the medical attention she needs.
Speaking after the tragic discovery last month, Detective Inspector Wes Martin, from the force's CID, said they wanted to find the mother to make sure she is OK.
"She may be in need of urgent medical attention and she is our absolute priority at the moment," he said
On Monday a spokesman for the force added that enquiries are continuing.
Detectives have been examining CCTV and carrying out house-to-house enquiries in the surrounding area, but so far have been unable to find the mother, despite promises to give her vital medical support.
Anyone with information can call West Midlands Police on 101, quoting incident number 1963 of May 20.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org.