The policy, announced by Prime Minister David Cameron on Sunday, would allow council house tenants to purchase their homes at discounted prices. The Government has pledged to build one new affordable home for every home sold.
The policy is described by Shapps as a "second tranche" of the Affordable Homes Programme (AHP) and in a recent meeting he insisted that the policy will work.
"People have looked at this and quite rightly been sceptical. But on this occasion this is going to stack up," Inside Housing reported. "The reason we know this for sure is that the AHP has already been an enormous success."
Shapps was responding to recent criticism that the sale of housing at such a discount will not raise enough money to build new housing.
There is also rising concern that social housing supply will be further depleted, which will increase costs in the long term.
Cameron announced the plans to reintroduce the "right to buy" council house scheme at the opening of the Conservative Party conference, as part of a plan to "fire up" the British economy.
