Reports over the weekend suggested chancellor Rishi Sunak was planning to give buyers and sellers more time to benefit from the tax cut in the upcoming Budget.
Rightmove said an extension would allow between 120,000 and 160,000 additional property transactions to go through.
Extra time would also give sales agreed by the end of last year to complete before the rumoured new deadline in May.
Due to delays with the legal process, there are an estimated 412,000 sales agreed last year that have been held up and of those, 100,000 are expected to lose out if the deadline stays as 31 March.
Rightmove said the conveyancing process would still result in transactions that are unable to complete even if the stamp duty holiday is extended but said it would still provide relief for some.
Tim Bannister, director of property at Rightmove, said: “We know the stamp duty holiday was intended as a temporary stimulus for the market, but the delays we’ve seen in the homemoving process have been through no fault of the buyers and sellers who agreed a sale last year and who are now desperately trying to get their deals over the line.
“The delays have been a result of the huge number trying to go through, along with the many challenges of the people involved in the process working from home.”
He added: “If there was a six-week extension it should give the majority of the sales from last year the chance to complete in time.”