Green bin collections will be extended from their current 32-week service to cover 50 weeks of the year according to the council's proposal.
However, people would have to pay for the "improved and extended garden waste collection" in the new opt-in service.
Councillor Karen Shakespeare, cabinet member for public realm, said: "We know how much people value this service.
"We’ve listened to complaints from people who are frustrated with the current collection cycle, so we know many will be pleased to see us extending this to all 12 months of the year.
An improved and extended garden waste collection is set to be introduced offering residents the service nearly all year round.
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The proposals will involve the collections becoming a paid-for service, with costs finalised in the coming months.
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"Most councils already charge to cover the costs of providing this service. A new chargeable opt-in service would give people the choice whether or not to use it.
"We will be doing all we can to ensure the extended and improved service offers excellent value to our residents.
"The proposals will go through a full scrutiny process which will establish recommendations around charging, which we will of course consider before making a final decision on the cost to residents."
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.
