It is expected an official announcement will be made by Chancellor Rishi Sunak on 3 March during the Budget, according to The Times.
The rumoured extension would bring the end of the tax break in line with the easing of lockdown restrictions in the UK.
It is also expected that the Chancellor will announce plans to raise corporation tax.
A spokesman for The Treasury has said they could not speculate on tax ahead of fiscal events.
David Hannah, founder and principal consultant of Cornerstone Tax, said: “This news is big a win for the property industry and home buyers, especially given that without it thousands of purchases could fall through and many will pause their plans to buy houses as our research shows.
“The approaching end of the stamp duty holiday is already having a profound effect on the property market, sale collapses are approaching record highs and solicitors and conveyancers are already reporting that they expect to see a considerable drop in demand very soon.
“While calls to make the holiday permanent or scrap the tax altogether seem unrealistic given the levels of public debt and the £12bn tax take it generates each year, this extension will delay the strict cut-off point, but the new date is a temporary fix to the issue.
“Raising to the nil-rate band, to somewhere around £300,000, will benefit the majority of buyers without affecting a large amount in tax revenues, which is obviously key to the recovery of public finances.
“These statistics demonstrate the importance of keeping the market moving to other sections of the economy and first-time buyers, those likely to spend less than £300,000, are the driving force behind this movement.
“Home ownership is key to the UK economy, upward mobility and the aspirations of many that are currently struggling to get on the property ladder.
“Not only this, but making it easier to move house without being penalised for doing so will make it easier to move to areas of growth and where jobs are.
“Especially important as we see a de-urbanisation and migration away from cities in the wake of the pandemic.”
Guy Harrington, chief executive of Glenhawk, added: “Whilst a short extension was inevitable given the backlog of transactions, stamp duty has been a strong revenue generator for the government and at a time when it can ill afford to be bleeding money, this is not a long term solution.
“As with Help to Buy, a tapering of sorts would ensure that the relief continues to benefit those most in need, whilst avoiding a situation similar to after the first lockdown where transactions fell by as much as 50%.
“A housing market correction would only further add to the already considerable economic woes facing UK consumers.”
Mark Hayward, chief policy adviser at Propertymark, says the speculation of a stamp duty holiday extension is good news for the industry.
Hayward said: “Today’s speculation that the stamp duty holiday will be extended is good news for the property sector.
“Since the holiday was first announced, we have continually worked to galvanise the industry and lobby government to rethink these timings due to our concerns that a cliff edge in March could cause thousands of sales to fall at the final hurdle and have a knock on and drastic effect on the housing market which has recovered well from the COVID-19 slump.
However, extending the holiday until June will create another cliff edge.
“We know from our own research that the majority of estate agents expect to see an increase in the number of failed sales if the stamp duty holiday ends at a cliff edge so we need government to consider a tapered end to the holiday so that buyers aren’t forced to pull out at the last minute and the property market can continue to thrive.”
Karen Noye, mortgage expert at Quilter, said: “News in The Times today that the stamp duty holiday is set to be extended in next week’s budget will be music to much of the housing market’s ears.
“The scheme has done wonders for the property market during this period of economic inactivity, vastly increasing the number of house sales and their prices with it.
“If this proves to be the case it will no doubt be good news for many, however it does simply kick the can down the road in terms of some of the structural problems in the housing market.
“During the first lockdown, estate agents were closed and the housing market all but ground to a halt.
“The stamp duty holiday played a fantastic part in reviving the market and getting it motoring again but this artificially increased house prices, making the mammoth task of getting on the housing ladder that much harder for younger generations who were already struggling to find money for a deposit before house prices rose steeply this year.
“It is likely that come June we will see more pressure to keep the stamp duty holiday in play to stop the inevitable house price correction that will come in the future as the economic realities of the pandemic bite.
“While this news helps to avoid the looming cliff edge for lots of buyers, it does just move it a few miles down the road and many will be in a similar position come June.”