Currently, people can get an unlimited number of free lateral flow tests, with the public urged to test twice a week. Those with symptoms can request a free PCR test.
Under a proposed new system, free lateral flow tests will only be available for high-risk settings such as care homes, hospitals and schools, according to the Telegraph.
Other countries in Europe, such as Germany and France are moving to end universal free testing this month.
The UK carries out more tests than many of its counterparts.
A Whitehall source told the newspaper: “It’s agreed that universal access isn’t sustainable or necessary given high vaccination levels.
“We now need to decide what the parameters should be that reasonably qualify access to free testing.”
NHS Test and Trace, the body set up to oversee testing, had a budget of £37 billion over two years, according to a report from the House of Commons’ Public Accounts Committee published in March.
The Treasury is believed to be for the ending of mass testing as more than 90 per cent of adults have now had at least one jab.
However some experts are wary as cases are still regularly topping 30,000 a day.
On Friday, a further 36,060 Covid infections and 127 deaths were reported in the UK.
Britain has one of the worst infection rates in the world, new data showed.
The UK’s total death toll comes to 137,541.
This week the government announced the removal of 47 countries from the red travel list, with just seven remaining.
The new changes will be put in place at 4am on Monday.
South Africa, Brazil and Mexico were among the countries to be moved off the list.