The Crimestoppers charity said it was offering the reward for information leading to the arrest and conviction of anyone responsible for offences linked to the baby boy’s death.
Police are still attempting to trace the mother of the infant, whose body was found near Willenhall on May 20, amid concerns for her welfare.
Detective Inspector Wes Martin revealed on Thursday that pathology reports suggested the baby could have been alive for several hours, although he was likely not alive when put into the Wyrley and Essington Canal in Rough Wood country park
He said: "We're treating it as a murder investigation until we've spoken to the parents who can help us with our understanding."
It is thought the boy may have been in the water for up to four days before a passer-by discovered him at around 1pm in a stretch of canal off Hunts Lane.
Mick Duthie, director of operations at Crimestoppers, said: “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.
“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.”
The baby's body has been "retained with dignity" in case the parents wish to lay him to rest, West Midlands Police said.
The force said the parents would be supported but that it was important to track them down to establish what happened.
Mr Duthie added: “Everyone who contacts Crimestoppers stays 100 per cent anonymous. Always. We have kept this promise for over 32 years.
“When you call our UK Contact Centre on freephone 0800 555 111, which is open 24/7, or use our simple, secure and anonymous online form at www.crimestoppers-uk.org to give information, nobody will know you contacted us, only you.”
The baby boy’s death followed separate discoveries of an abandoned newborn in a Birmingham park and a youngster who was found dead in a Morrisons car park in Bilston.