According to the BBC, Deputy First Minister Nicola Sturgeon is expected to confirm the news.
The scheme, which was first introduced in 1980, allowed council tenants to buy the homes they rent at a discounted rate.
Since "right to buy" was introduced, 455,000 Scottish properties have been sold under the scheme.
The Government has already abolished the scheme for new tenants, but it is thought it will be scrapped altogether by 2016.
In November last year, a Scottish Government consultation found that a majority of local councils wanted the policy to come to an end, as did a number of tenants and social landlords.
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As a result of the scheme, the number of homes available for cheap rent has reduced, and increased the waiting lists for properties of this type.
Speaking to BBC Radio Scotland's Good Morning Scotland programme, Leader of the Scottish Conservative Party, Annabel Goldie, said she opposed the move.
She added: "I can still remember the days when people lived in monolithic council house schemes - that is what they were called - and they were afflicted by a postcode prejudice.
"They were apprehensive about disclosing their address because they felt it would negate their chance of getting a job or even being accepted for an interview.
"By offering a tenant the right to buy, you did two things - you first of all introduced a freedom to the individual to make a choice about how they wanted to live, and secondly you stopped them being trapped in that environment - because that is exactly what they were."
The announcement regarding the future of the 'right to buy' scheme is expected to be unveiled after Ms Sturgeon makes a visit to tenants at Queens Cross Housing Association.
(JP/CD)
