Plans to empty bins every two weeks in Wolverhampton
Bins would be emptied fortnightly instead of weekly in Wolverhampton under plans to save up to £2.4m a year.
People could have a larger brown bin to cater for more recyclable waste under the proposal, the council said.
A five-year £2.3m government grant that enabled maintaining weekly collections would end in April, it added.
The government said it was still providing a long-term funding settlement to the city of more than £850m to spend between now and 2020.
A Department for Communities and Local Government spokesman said: "This will allow them to deliver high quality services whilst keeping council tax bills down."
Plans have been put forward to increase opening hours at the city's two household waste and recycling centres.
Proposals also include charging £35 a year for a garden waste service and ending a food waste recycling service not used by 80% of Wolverhampton households, the city council said.
It said it must make an estimated £54.6m of new cuts by 2019-20.
Cabinet councillors, who meet on Wednesday, will be asked to agree to consult with the public on 32 proposals that would contribute £13.5m towards that total.
The annual £11.5m cost of household waste and recycling services was "no longer affordable when Government funding cuts are forcing the council to review the way every service is delivered," the authority said.
It said there were other issues also driving the need to change, such as more people renting and more single-person households.
The government said by the end of this parliament, councils would be able to keep 100% of local taxes including all £26bn from business rates.
It added it would continue to keep residents' bills down with council tax still expected to be lower in real terms in 2019-2020 than it was in 2009-2010.