Police have yet to trace the mother of the infant, who was born full term, amid growing fears for her well-being.
Investigators believe someone may know or suspect who the mum is and have urged anyone who can help to come forward.
The baby was “probably not alive” when he was put into the Wyrley and Essington Canal in Rough Wood country park, near Willenhall, Walsall.
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He could have been in the water for up to four days before being found, West Midlands Police said.
A member of the public discovered his body around 1pm in the canal, off Hunts Lane.
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Crimestoppers is offering the reward for information leading to the arrest and conviction of anyone responsible for offences linked to the death of the baby.
Director of operations at the charity Mick Duthie urged anyone who can help to come forward.
“This is a particularly sad, tragic case and shocking for the community, so we are keen to have answers as to what happened and who was involved,” Mr Duthie said.
“We are urging anyone who may know something to contact our charity anonymously as soon as possible. There is concern also for the well-being of the baby’s mother.
“Investigators, who have asked our charity to put up this reward, believe that someone may know or suspect who the mother is.
“We hope that our reward for information given anonymously will help prompt someone’s conscience to speak up and tell us what they know.”