Travel industry groups have called for all remaining Covid restrictions on travellers to be removed in the latest government review.
With data last week suggesting one in 25 people in the UK currently had the virus, airlines say passenger testing is having no real impact.
It is thought ministers are finalising changes to guidance on Covid testing.
The travel industry said compulsory testing for UK arrivals and departures had held back the sector’s recovery.
The prime minister will meet his cabinet later and urge them to back his decision not to impose any further Covid restrictions in England.
The BBC understands the government is discussing the removal of advice that people who test positive on a lateral flow device should seek a confirmatory PCR test.
On Tuesday, Boris Johnson said he hoped the country could “ride out” the current wave, although he acknowledged parts of the NHS would feel temporarily overwhelmed.
The government has said it continued to “keep all measures under review”.
What are the current travel rules?
Currently, all travellers to the UK aged 12 and over have to show proof of a negative test, which can be a PCR or a lateral flow test, and must be taken up to two days before departure for the UK.
They then have to take another test – which this time must be a PCR test – within the first two days after their arrival in the UK.
But at the time that rule was brought in a month ago, the number of new cases reported in the UK each day was running between 40,000 and 50,000 – and was only rising relatively slowly because it was almost entirely made up of the Delta variant of Covid.
But now, the UK has announced more than 200,000 new cases in a day for the first time in the entire pandemic and Omicron is the dominant variant – so airlines can argue that there is no longer any hope of relying on testing to “keep out Omicron”.
