The authority says the change will make support for low-income households more stable and predictable.
The current scheme is means tested, which adjusts as incomes change, meaning it can be difficult for households to plan and budget.
The proposed new ‘banded’ model will provide steady relief for those with low or fluctuating incomes.
But the council says some households will be negatively impacted.
The authority is encouraging everyone currently eligible for the existing scheme to give their views.
The online consultation closes on Friday, the 13th of December.