The Labour-run council is one of three authorities undergoing central government scrutiny of its local plan process.
At a meeting next Monday, the council's cabinet is being asked to consult on including a series of housing and employment sites in its new draft local plan, including 48 sites on green belt.
It follows a review of the council's potential capacity for new housing and employment sites.
A report by officers says that the council's housing need figure, using the government's new standard method, is 803 homes a year, which equates to 12,045 homes over the 15-year plan period up to 2033.
Beyond the sites currently identified, including those with planning permission, the report says there is a shortfall of 4,794 homes over the plan period. "Previously undeveloped land in the green belt has so far been excluded from these calculations," the document adds.
"The review concludes that there is a continued shortage of land for development within the urban area to meet the needs of the local population and the economy; and that it would not currently be possible to meet these needs within Wirral without using land within the existing green belt; and identifies the sites that could potentially be considered suitable for release from the green belt through the local plan," the report says.
It goes on to say that Wirral's neighbouring local authorities have "already indicated that they would all be unable to provide for any of Wirral’s identified needs", adding: "This report concludes that there is currently no other realistic alternative to reviewing the potential of land in the green belt to meet the shortfall in the borough’s housing land supply, if the council is to submit a sound and legally compliant local plan to the secretary of state."
The council has published a list of housing and employment sites that it says it will consult on for six in September.
These would then be included in an "initial draft local plan" to be reported to the cabinet in December 2018. This draft would include a final housing requirement and a decision on "whether the exceptional circumstances necessary to alter green belt boundaries have been demonstrated".
The sites listed include 48 green belt sites across the district, whose size and housing capacity is not stated by the council. More details on the review's findings will be published in September, the report adds.
In addition, there are 91 urban brownfield sites without planning permission listed, including 1,100 homes at the proposed Wirral Waters development.
According to the document, the council expects the final draft local plan to be ready by July 2019 and to submit it for examination in September 2019.
The report warns: "A failure to meet the council’s published timetable for the preparation of the local plan could lead to intervention by the secretary of state, including potential financial penalties, which could include the withdrawal of some or all, of the council’s annual award of New Homes Bonus or by consultants appointed by the secretary of state in default."
George Davies, deputy leader and the cabinet member for housing and planning, said: "The government have set Wirral a target, which means we must make enough land available to allow for 12,000 new homes to be built in Wirral by 2035.
"We know, and so do government ministers, that we do not have enough brownfield or urban land to enable housebuilding of this scale.
"This is why we will be talking to residents through an extensive programme of community consultation over the coming weeks.
"We are legally obliged to review our green belt land and, while making any of those sites available for development will be our last resort, it has been made unequivocally clear to us that if we do not do it, it will be taken out of our hands."
Davies said that 46 per cent of Wirral is currently classed as green belt.
The report and accompanying documents can be found here.