The chancellor will use his Budget on 3 March to move the tax break in order to bolster the property market as the UK recovers from the economic impact of lockdown, The Times reported.
The government made a vast majority of house buyers exempt from paying the tax on properties worth up to £500,000 until the end of March, allowing people to save up to £15,000 in tax.
The paper said extending the policy could cost the Treasury around £1bn.
It also reported that Mr Sunak was expected to extend the furlough scheme, which is set to end on 30 April, until the end of June as people could return to work – at a potential cost of £4bn each month.
The government has already spent £300bn on coronavirus measures to shield the economy over England’s three lockdowns.
It comes after the right-leaning Centre for Policy Studies (CPS) urged Mr Sunak not to end the stamp duty holiday.
A report by the centre said the tax break had increased house sales to their highest level since before the 2007 financial crisis.
Data shows that after an initial decline in sales between April and June 2020, the number of transactions increased from 132,090 in the second quarter to 225,870 in the third quarter and 316,300 by the end of quarter four – the highest level since 2007.
The think tank’s research shows that stamp duty revenues actually rose by 27 per cent in Q3 compared to Q2, from £1.1bn to £1.35bn, and suggests they will rise again in Q4 given the continued increase in transactions.
The think tank called on the government to either permanently increase the threshold on primary residences to £500,000 – at a cost of £3bn – or abolish it altogether.
Additional reporting by Press Association