Housing minister Alok Sharma is examining the request, submitted by Treasury advisor Arlingclose on behalf of the authorities in June.
The proposals call for legislation to be changed to allow councils to spend money raised through Right to Buy sales on purchasing homes from the open market for shared ownership.
Councils are supposed to replace homes lost through the Right to Buy with new builds for affordable rent, but are only allowed to spend 30% of receipts on the construction costs.
Virtually all the homes sold under the Right to Buy are social rent properties, and the policy move would raise fears over the further depletion of social rented stock.
Figures released by the Department for Communities and Local Government (DCLG) last month revealed council homes are being sold off nearly three times faster than they are being replaced.
Since the 1980s when the policy was introduced, more than 1.5 million council homes have been sold under the Right to Buy. Councils were first allowed to spend receipts on replacements in 2012, and have since sold more than 54,000 homes and started just under 11,000 replacements.
In May, Inside Housing revealed only 48% of these replacements were social rent, with the remainder affordable rent - up to 80% of market rates.
Arlingclose is suggesting that the 30% receipts should be used to purchase part of an open market home, with the remaining portion of the equity bought by a local resident.
The buyer would then pay rent on the council's 30% share in a shared ownership deal, with councils able to use separate funding to top up the offer.
A spokesperson for the DCLG said: “We have received Arlingclose's correspondence and we are currently considering their proposals for the use of Right to Buy receipts.”
Oxford City Council, Swindon Borough Council, Bolsover District Council and North East Derbyshire District Council are among the 50 local authorities to support the proposals.
“The reality is that most local authorities really want to spend these receipts but they just aren't able to,” said Cecilie Booth, strategic director at Arlingclose.
“This model isn't perfect but it will help them to provide affordable housing locally and it is very easily done. It isn't going to solve all the problems but it will help local people rather than the money going back into the central pool.”