The red list will be cut to just seven countries from Monday, but travellers from those destinations will still need to quarantine at a government-approved hotel for 11 nights at a cost of £2,285 per person.
Ministers are set to discuss proposals to axe the hotel quarantine programme at a Covid-O cabinet meeting, according to The Times.
Transport Secretary Grant Shapps is said to be in favour of allowing travellers to complete their quarantine at home.
But other ministers, including Health Secretary Sajid Javid, are against the idea.
Government advisors have argued for hotel quarantine to stay in place in case a new variant emerges that could evade vaccines.
Currently 90 per cent of Britons have had at least one jab.
Downing Street has denied that there were plans to scrap the policy and government sources told the newspaper that it is likely to remain until the end of the year.
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.
The Department of Health and Social Care, which is responsible for controlling the managed quarantine service, said that it was kept under constant review, adding: “We are committed to protecting our country and the progress of our phenomenal vaccine rollout against the risk of new coronavirus variants, and there are no plans to end the managed quarantine service.
“We have taken decisive action at the border with our managed quarantine system and every essential check we’ve introduced has strengthened our defences.”