Don Valley Stadium - home to Olympic champion Jessica Ennis - could be demolished under cuts announced by Sheffield Council.
The Labour Council Leader has criticised the Government for imposing the cuts - shaving £50m from their 2013-2014 budget.
Council leader Julie Dore said the cuts were going "further and deeper", and the budget proposals will lead to "massive changes for the city."
Demolishing the Don Valley stadium would save £700,000 a year and allow the authority to avoid having to invest the £1.6m required over the coming years.
It is proposing to reopen and refurbish Woodburn Road stadium.
Stocksbridge Leisure Centre will also close and £10.5m will be cut from care for the elderly and vulnerable.
Other cost-cutting measures include closing 14 of the city's 27 libraries.
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A murder investigation is underway in Rotherham following the death of a teenage girl.
Police say that unless one outstanding line of enquiry provides a breakthrough, the investigation will be scaled down next month.
South Yorkshire Police are continuing to question an 18-year-old man on suspicion of murder following the death of a teenager yesterday.