Ministers are to increase the maximum discount - currently £16,000 to £38,000 - to more than the expected £50,000.
They hope it will persuade more tenants and mortgage lenders to get involved in the scheme first started in the 1980s.
But housing charity Shelter says the plans risk diminishing the stock of "genuinely affordable" social housing.
It also says the plans could saddle low-income families with mortgage debts they cannot afford.
The "right to buy" scheme was first started under Margaret Thatcher's government.
In December the government launched a consultation on "re-invigorating" the right to buy, which has dwindled in recent years, and suggested the maximum discount may be raised to £50,000.
Currently, discount levels differ across the country, ranging from £16,000 to £38,000.
Now ministers believe discounts should be as high as £75,000, the BBC understands.
The government insists all social homes that are sold "will be replaced on a one-for-one basis by a new affordable rent property, ensuring there is no reduction in the number of affordable homes".
But Shelter says it will still have the effect of damaging social housing.
Roger Harding, Shelter's head of policy, research and public affairs, said: "The government is not going to replace like-with-like.
"The 'affordable rent' model means landlords can charge rents of up to 80% of market rates, which is typically higher than council rents.
"The net result will be a reduction in the number of genuinely affordable homes for families on modest incomes."
He added: "That could have the added effect of pushing up the housing benefit bill, if there are fewer council houses and more 'affordable rent' properties with higher rental costs."
Mr Harding said: "We are also concerned that ownership is not necessarily the most financially suitable form of tenure for a lot of social housing tenants.
"Many are on very low incomes and could find themselves unable to afford the mortgage repayments. Statistically, right-to-buy mortgage holders are far more likely than other purchasers to have their homes repossessed."
Later this week Housing Minister Grant Shapps is expected to say: "This coalition government backs the dreams of those who want to own the roof over their own head."
He has promised to triple or even quadruple the discounts available to "hard-working families".
Mr Shapps will say: "New home buyers will have the satisfaction of knowing that for each property sold, we'll be aiming to replace it with a new affordable home for the record numbers left languishing on Labour's housing waiting lists.
"It's a win/win that backs aspirational council tenants whilst dealing with the legacy of Labour's record waiting lists."
Social housing tenants could be offered discounts of up to £75,000 under plans to increase the numbers exercising the "right to buy" their home in England.