The move, which would see self-isolation swapped for mandatory testing, would likely come into effect in August, a government source told The Times.
Confirmation is expected to be announced on Thursday 24 June as part of the latest Department for Transport review of international travel.
At the same time the UK’s “traffic light” system will be updated, with the government revising its green, amber and red lists for travel.
At present, ministers are advising against holidays to anywhere not on the green list.
However, expectations are low that many, if any, new destinations will go green on Thursday after the last review saw nothing added and Portugal removed.
Only a “handful” of countries are in contention to be added this time around, according to government sources.
The Health Secretary raised hopes of holidays for double jabbed Brits further by saying he was “in favour” of replacing quarantine with daily testing.
Matt Hancock told BBC Breakfast: “We’re not ready to be able to take that step yet, but it’s something that I want to see and we will introduce, subject to clinical advice, as soon as it’s reasonable to do so.”
Asked whether such plans could be in place by August, Mr Hancock told LBC that: “We’ll get there when it’s safe to do so.”
At present, a traveller’s vaccination status makes no difference to the restrictions they face when entering the UK.
Those arriving from an amber list country must self-isolate for 10 days and take two PCR tests regardless, while those from red list countries must shell out for 11 nights in a government-mandated quarantine hotel.
It follows the news that fewer than one in 200 people returning to the UK from “amber list” countries are testing positive for Covid-19.
Data from NHS Test and Trace also revealed that no virus variants of concern were found in any of the travellers entering the country from the 167 destinations currently graded “amber” by the British government.
Between 20 May and 9 June, just 89 of the 23,465 passengers arriving from amber countries tested positive for the virus.