According to reports ministers are planning to replace it with a new system after the scheme expires in 2021.
It is expected the new arrangement will focus on helping out the lower-paid, rather than giving “handouts” to the middle classes.
Official figures this year revealed the average wage of somebody supported by Help To Buy is £55,000 – more than double the average wage of £26,000.
Since its launch in 2013 the Government has provided more than £8.9billion of support.
The scheme has been extended to last until 2021 with an additional £10billion already pledged.
The programme has come under fierce criticism at a time when public finances remain tight.
Matt Kilcoyne, from the Adam Smith Institute think tank, said: “Scrapping the scheme is a good step toward a housing market that works for everyone.
“The well-off shouldn’t get a handout from government that pushes up the price of houses in already expensive markets.”