The authority said it would also make £27m of cuts to adult social care and £6.7m in children's services and education under initial proposals.
The Labour-run council is also planning to axe school crossing patrols, cut back on early years speech therapy and increase council tax by 4% a year.
It said it would face a budget gap of between £40m and £75m.
Sir Richard Leese, leader of Manchester City Council, said: "Manchester remains an ambitious city and this will be ambitious budget which will nevertheless involve some difficult decisions.
"We have to do services fundamentally differently to the way we do [them] now."
He said devolution, which gave the city "greater autonomy" in areas such as health and social care, would help it to make the changes by placing "greater emphasis on prevention of problems, not spending fortunes on tackling them reactively".
"In particular, we have to give people more support early on, more support in the communities they live in, rather than admitting them unnecessarily in hospital like we do now.
He added: "These are options and no decisions about specific proposals are being taken until the New Year."
Manchester's sole opposition councillor, Liberal Democrat John Leech, said people would be "understandably shocked and frustrated" at the job losses just weeks after a number of senior managers were awarded above-inflationary pay rises.
"Whilst I accept the cuts to Manchester are tough, there seems to be little attempt to lessen the blow on local residents and frontline services."
Consultation on the proposals will begin next month.
The authority said its resources had reduced from £682m a year in 2010/11 to about £528m a year, with a 40% reduction in the workforce.
Manchester City Council is set to cut 160 jobs as part of plans to save up to £75m over the next three years.