Transport Secretary Grant Shapps is expected to scrap the arrival tests in time for the school half-term holidays in February.
The move would mean families can return from abroad without having to take a lateral flow test on day two of their arrival back in the UK, which is currently required under government rules.
When could an announcement be made?
Mr Shapps is understood to be in favour of ending the testing regime for the fully vaccinated in time for the February half-term holidays.
It is expected that an announcement on the changes will be made on 26 January, when Plan B restrictions in England are due to expire.
A source close to Mr Shapps is said to have told The Sunday Times: "We are looking at removing all Covid tests for vaccinated travellers by the end of January, which is likely to coincide with the review of the plan B measures on January 26.”
The decision to scrap testing on arrival will come as a welcome relief to the travel industry, and will follow the relaxation to pre-departure testing rules earlier this month.
Recent changes mean travellers no longer have to take a pre-departure test before returning to the UK, while day two PCR tests and self-isolation on arrival have also been scrapped.
Instead, fully vaccinated travellers currently only need to take a lateral flow test on day two of their arrival, and only need to self-isolate if the result is positive.
Those who are unvaccinated are still required to quarantine at home for 10 full days on arrival in the UK, and must take a PCR test on day two and day eight.
What other Covid rules could change?
The Prime Minister is expected to scrap Plan B Covid restrictions in England later this month, which were put in place to slow the spread of the Omicron variant.
The rules are due to expire on 26 January, subject to a eview, but scientists appear to have provided evidence that support the lifting of rules.
Modelling included in new Scientific Advisory Group for Emergencies (Sage) documents released on Friday (14 January) suggests that restrictions would make little difference to hospital admissions.
As such, it is likely that the current rules, which include use of Covid passports to enter certain venues and events, will be scrapped.
This will mean people will no longer have to show proof of their vaccination status or a recent negative test to gain entry to nightclubs and large venues and events, while work from home guidance is also expected to lift.
The only rule that may remain in place is the use of face masks in indoor venues and on public transport.
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