Tanya Lyon, the council’s community safety manager, said fly-tipping was taken “very seriously” with perpetrators fined up to £1,000 or prosecuted.
She said the council was working alongside its waste disposal company to put warning signs on the recycling bins and the viability of installing CCTV was also being considered.
She added: “On private land, fly-tipping will be investigated, but landowners are responsible for clearance.”
The Local Democracy Reporting Service said it understood Morrisons had been in contact with the council over the issue, but the supermarket chain had declined to comment further.
Meanwhile, councillor Emily Nelson, Labour’s ward member for Westfield, said anyone with information that could help with taking action against the fly-tipping should come forward.