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.”
Ireland is pledging emergency legislation enabling it to send asylum seekers back to the UK.
More than 80% of recent arrivals in the republic came via the land border with Northern Ireland, Irish justice minister Helen McEntee told a parliamentary committee last week.
Ireland’s deputy prime minister has said the threat of deportation to Rwanda is causing migrants to head for Ireland instead of the UK.
Micheal Martin said the policy was already affecting Ireland because people are “fearful” of staying in the UK.
The former taoiseach told The Daily Telegraph: “Maybe that’s the impact it was designed to have.”
Simon Harris, Ireland’s latest leader, has asked Ms McEntee to “bring proposals to cabinet to amend existing law regarding the designation of safe ‘third countries’ and allowing the return of inadmissible international protection applicants to the UK”, a spokesman said.
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Ms McEntee said she will be meeting UK Home Secretary James Cleverly in London on Monday.
“There are many reasons why we have seen an increase in migration towards Ireland,” she told RTE.
“My focus as minister for justice is making sure that we have an effective immigration structure and system.
“That’s why I’m introducing fast processing, that’s why I’ll have emergency legislation at cabinet this week to make sure that we can effectively return people to the UK, and that’s why I’ll be meeting with the home secretary to raise these issues on Monday.”
People are now “worried” about coming to the UK, Rishi Sunak has said.
He told Sky News: “If people come to our country illegally, but know that they won’t be able to stay here, they are much less likely to come, and that’s why the Rwanda scheme is so important.”
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Are migrants fleeing from UK to Ireland?
Mr Sunak said the comments from Irish politicians show that “illegal migration is a global challenge”.
“[That] is why you’re seeing multiple countries talk about doing third country partnerships, looking at novel ways to solve this problem, and I believe [they] will follow where the UK has led,” he said.
Shadow minister Wes Streeting said it was unlikely a Labour government would bring people back from Rwanda if some are sent there.
“Once people are settled in Rwanda, they’re settled in Rwanda,” he told Sky News, adding it was doubtful that Labour would “unpick that situation”.
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Regarding illegal migration in general, he said it required “putting the money that’s gone to Rwanda into the National Crime Agency so we can have proper cross-border policing to tackle the criminal gangs, speeding up the processing of decision-making, making sure we’ve got serious returns agreements with other countries”.
The duke is expected to provide a reading at the event, which marks a decade since the inaugural Invictus Games in London in 2014.
The games were founded as a sporting event for injured and sick military personnel and veterans.
Actor Damian Lewis is set to recite the Invictus poem during the service.
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Representatives from across the Invictus Games participating nations, including members of the wounded, injured and sick service personnel and veteran community, will also be in attendance.
Fire and ambulance services also attended, Durham Constabulary said.
Detective Chief Inspector Mel Sutherland, who is leading the investigation, said: “Officers are keen to speak to anyone who was travelling on the A19 at around 12.20pm to 12.30pm who may have mobile phone or dashcam footage which captures the moments leading up to the incident.
“Our thoughts remain with the man’s family at this time.”