The Chancellor, Rishi Sunak, is believed to be discussing ways of extending three month mortgage holidays with regulators and banks.
The Financial Times reports the government hopes to prolong the scheme for borrowers struggling with payments because of the impact of coronavirus.
More than 1.6 million mortgage customers have taken advantage of the relief from making payments.
The banking body, UK Finance, estimates this is an average of £755 a month.
The government brought in the mortgage break scheme in mid-March, which allows people to apply to defer their payments, without their credit reference being affected.
That respite from payments would end for the first applicants in June.
This is not free money. It will still have to be paid back later on, so mortgage customers will face higher bills once the so-called holiday comes to an end.
The problem the Treasury is grappling with is that an abrupt end to the scheme could produce a cliff-edge effect, with families facing money problems as bad, if not worse, as they did when the virus struck.
A spokesman for the financial regulator, the Financial Conduct Authority (FCA,) would not comment on any talks but said it was vital that customers should have advice and support at the end of a payment freeze.
He said: "We are currently considering what support will be needed for customers reaching the end of a mortgage payment freeze. We have not yet made any final decisions but we will make an announcement soon."
One idea is that the mortgage scheme would be extended for a further three months, but that there would be no blanket extension and the rules on applications could be tightened.
A spokesman for the Treasury said: "We're not commenting on speculation."