The cuts aim to help the city meet a £156m savings target over the next three years following reductions of £173m across services over the past three years.
Mayor Joe Anderson said all "discretionary" services, which the council is not legally bound to provide - including parks, leisure centres and regeneration - are to find budget savings of 50 per cent.
"This is really unpalatable and not what I or any of my team came into politics to do," he added. "People will be worried about how they may be affected and the truth is that it will impact on every service. The stark reality is that it will mean less of absolutely everything."
A city council representative said: "The details of the budget haven't been decided and how the savings will be made with parks and other services has yet to be determined. But the annual parks budget is around £10m and the department will be asked to save 50 per cent over the next three years.
"We expect more details to emerge around February or March." The city's budget meeting is on 5 March.
Last week the council announced a 25-year deal with Formby Hall Golf Club to operate North Liverpool and Allerton golf courses with Glendale Golf to save the £1.7m over five years.
Elsewhere, Torbay Council has outlined plans to cut £190,000 from its green-space budget in the 2014-15 and 2015-16 financial years.
It wants to cut £90,000 from its natural environment and sports club budget and £70,000 from green space maintenance, while it expects to save £30,000 from arboriculture in a move away from planned maintenance to a reactive service.
The decisions are described in the proposed budget as "minor" but the budget papers admit there is "a potential for public dissatisfaction" as well as reduced park inspections and monitoring of contractors.
To save another £210,000 the council has struck a deal with contractor Tor2, a collaboration between the council and Kier responsible for a wide range of services including park maintenance and beach cleansing.