Chiefs said the white vehicle had been used to dump the items and other waste on three separate occasions in the area during September this year.
Efforts to trace the vehicle have not been fruitful, with members of the public now being asked to come forward if they have any information.
Councillor Garry Perry, deputy leader for resilient communities said: "If you provide information that leads to a successful prosecution, you may be eligible to claim a £500 reward.
“Clearing and disposing of illegally dumped waste costs the council hundreds of thousands of pounds a year.
"This isn’t the council’s money though — it’s public money and could go a long way to supporting our vulnerable residents, particularly during these extremely challenging times.”
People should contact the Community Protection team at Walsall Council on 01922 653060 or by emailing CommunityProtection@walsall.gov.uk quoting reference WK/ 202230135.