The authority said it had "little choice" but to consider the rise which will result in an extra £55 a year for a band D property.
Children's Services will lose £8.9m and 51 jobs will go under the proposals.
The city council said it has a funding shortfall of £54m due to government cuts and rising costs.
However, Sir Richard Leese, leader of Manchester City Council, said the "headline savings figure this time round is smaller, mostly due to our prudent planning" and the dividend from its shareholding in Manchester Airport Group.
He said devolution was "not a magic bullet" and it would still have funding challenges.
Sir Richard said it would allow the authority "greater control" to help "support better integrating services" which would help people become "more independent and less reliant on the most expensive public services".
The plans will be considered at a scrutiny meeting and an executive meeting before a final budget is set in March.
Manchester City Council is planning to make cuts of £13.8m from next year's budget and increase council tax by almost 4%.