The body estimates that 80,000 out of the 88,000 homes expected to be sold due to the Right to Buy scheme by 2020 will not be replaced.
The LGA said that some new housing measures, such as the loss of £2.2 billion from council housing budgets by 2020 as a result of social housing rent cuts, risk making building replacement homes "all but impossible".
Town hall leaders forecast that 66,000 council homes will be sold to tenants under the existing Right to Buy (RTB) scheme by the end of the decade, but the LGA said that "complex rules and restrictions" make it hard for councils to quickly replace the majority of homes sold.
Councils keep a third of sale receipts to build new homes - but they have argued that they should be allowed to retain 100% of receipts locally.
The LGA predicts councils could be forced to sell a further 22,000 "high value" homes to fund the Government's plans to extend Right to Buy to housing association tenants - adding that this number could be higher depending on the definition of high value.
The body argued that the Government should fund the Right to Buy extension by giving councils the power to help raise £13 billion by building more homes on surplus public land rather than forcing the sale of other valuable homes.
The LGA warned that a fall in affordable council rented housing would drive up the housing benefit bill by an estimated £210 million by the end of the decade as more families will end up moving into the more expensive private rented sector.
Cllr Peter Box, the LGA's housing spokesman, said: "As a minimum, we forecast that 88,000 council homes will be sold up to 2020."
He continued: "Councils have long called for the ability to replace housing sold through Right to Buy quickly and retain 100% of receipts from all sales.
"This is imperative to ensure that councils can reinvest in rapidly building the homes that people in their areas desperately need."
A Department for Communities and Local Government (DCLG) spokesman said: "The LGA figures are misleading and based on speculation, more council housing has been built since 2010 than in the previous 13 years.
"More homes were built as a result of Right to Buy, under the first year of the reinvigorated scheme - showing councils are delivering on their commitment to provide a new affordable property within three years.
"The Housing Bill ensures the sale of empty high value council assets will enable receipts to be reinvested in building new homes that better meet local needs as well as supporting home ownership through Right to Buy."