The council is proposing to cut £33 million, which would hit libraries, theatres, schools and museums.
Spending on the Theatre Royal and the Royal Concert Hall will be slashed by two thirds – but the Royal Centre would become an independent trust, allowing it to apply for grants.
The council has also revealed that Carlton Road library could close, in addition to the closures of St Ann's and Bulwell libraries announced previously.
Opening hours at Newstead Abbey, Brewhouse Yard Museum and Green's Windmill and Science Centre, in Sneinton, could be reduced.
The council is considering cutting the workforce by about 370 posts next year, saving more than £11 million.
Funding for capital projects such as roads, schools and housing has also been reduced or scrapped.
City council deputy leader Graham Chapman said: "We have been among the most successful councils in protecting jobs and frontline services but because of the scale of these cuts, there will inevitably be some significant impacts. We are approaching the Government about the damage another settlement like this next year would inflict." Proposals will be discussed by the executive board on Tuesday and ratified at full council on March 7.