The Department for Communities and Local Government (DCLG) has tasked a team from the London School of Economics (LSE) to evaluate the scheme, according to industry journal Property Week.
Both scrapping the scheme entirely or introducing a tapering system are being considered, the reports said.
A spokesperson confirmed the government has committed to working with the sector to review the future of the scheme.
It also added: “We also recognise the need to create certainty for prospective home owners and developers beyond 2021, so will work with the sector to consider the future of the scheme.”
The end of Help to Buy would have huge implications for British property prices.
The Help To Buy equity loan scheme has helped more than 100,000 people to get onto the ladder.
Around 38 per cent of private completions make use of the scheme, according to Thomas Buisson, an analyst at stockbroker Liberum.
Meanwhile, government figures from 2015 show the Help to Buy Equity Loan had contributed 14 per cent of total new build housing output.
As news of the possible end of Help to Buy hit the market, shares in FTSE 100-listed builders Barratt, Taylor Wimpey and Persimmon fell by around five per cent each in early trading. FTSE 250-listed Bellway and Crest Nicholson had fallen by more than four per cent and 3.5 per cent respectively at 9.30am this morning.
Communities secretary Sajid Javid published a white paper in February which seemed to bolster the Help to Buy scheme.
It said: “We have committed £8.6 billion for the scheme to 2021, ensuring it continues to support homebuyers and stimulate housing supply.”
Removing this significant support to demand for homes would likely damage house buyers, hence why the markets have reacted as they have.
Thomas Buisson said: “Removal of the scheme would impact margins and sales rates” for housebuilders.
“The government has already shown its willingness to make changes to the scheme, after it last month said it will limit the use of Help to Buy for leasehold purchases (where the rights of ownership are time limited, albeit usually for a very long time). Leasehold purchases can lead to extra fees for owners to the person who owns the freeholder.
The government’s spokesperson said: “As a government committed to building a fairer society, we’re taking action to stop the unfair use of leaseholds. This includes, as far as possible, removing the Help to Buy Equity Loan on new build houses where they are sold as leasehold.