A report by The Daily Telegraph on the weekend said Sunak (pictured) was aware that thousands of purchases could fall through if the hard 31 March deadline were maintained.
As a result, the chancellor is contemplating an extension until mid-May to allow those cases to complete, the Telegraph said.
However, it also reported that a longer extension or even scrapping of land tax, as many in the industry have called for, is unlikely due to the significant effect this would have on tax income for Treasury.
Data released last week showed that tax income from stamp duty on property purchases fell by more than £540m in the last three months of 2020 compared to the same period in 2019, despite a 14 per cent increase in sales.
Lenders have already begun issuing warnings that the rush to reach the end of March deadline could impact service levels for new business.
While last month conveyancers said it was becoming a lottery for which purchases would complete in time.
During a debate in Parliament earlier this month MPs called for a phased withdrawal of the deadline to help support borrowers in the process.
The upcoming Budget on 3 March would appear to be a likely date for any extension to be announced.
A Treasury spokesperson said the department did not comment on tax policy outside of fiscal events.