Council chiefs said the service could be extended from a 32-week service to cover 50 weeks of the year under proposals being considered.
It would mean people would have to pay for the "improved" service – with the fee expected to be revealed after the plan is scrutinised.
But the move has been heavily criticised by a senior Labour councillor, who said it was the "wrong time" and the "wrong policy" for the borough.
Councillor Parmjit Sahota, shadow cabinet member for public realm, said: "I'm totally against it. I've been inundated by messages from local residents about this. I think it's the wrong decision because it's charging people to go green – which the Government is urging us to do.
"It will lead to more fly-tipping. We should be incentivising people to go green and we [Labour] would not go ahead with this tax on being green – this is going to discourage them from going green.
"There's a lot of frustration out there and it has not been thought through. It doesn't make sense. I can't fathom why, now, they're asking people to pay for the service. It's the wrong time and the wrong policy."
Councillor Sahota said he had written to Councillor Karen Shakespeare, cabinet member for public realm, over the issue as he criticised the council for their handling over the Anchor Lane tip.
Residents in the borough – particularly in Coseley – were stopped from using the site, owned and run by Wolverhampton Council, from April 1 this year after an agreement was ended between both councils.
Councillor Sahota said it meant there was "no recycling" in the north of the borough and called the move to implement a charge for collections as something "which residents will see through".
Councillor Shakespeare, who holds the cabinet role at the Tory-run authority, said chiefs had listened to complaints from people who were "frustrated" with the current collection cycle.
She added the new chargeable opt-in service would give people the choice whether or not to use it, with most councils already charging to cover the costs of providing this service.
Currently, green bin refuse is collected every fortnight and stops during the winter months, but the new proposal would ensure weekly collection and would only stop around Christmas.
The proposals are set to go through a full scrutiny process before a final decision is made on the cost to residents, bosses have said.