It is understood this means there will no longer be amber or green list countries - but red will continue with travellers still needing to quarantine in hotels on returning from high-risk destinations.
People who have received both vaccines can already visit amber countries without having to quarantine on their return.
The proposed new system is only likely to effect those who are not vaccinated.
The rethink comes after the government’s promise to review the system by October 1.
“It’s about whether you are vaccinated or not, rather than the country you are travelling to,” a source briefed on the proposal told the Telegraph.
“What it means is that green and amber disappear and only vaccination status will count for where you travel. For a vaccinated person, just as now all countries apart from red are ‘green’.
“For an unvaccinated person, it means that your travel to a green country might be slightly more difficult. There’s a potential psychological boost in that a lot of people think travel to amber is risky whereas if it disappeared, people may be more willing to travel to X, Y or Z.
“It could also incentivise people to get vaccinated. There’s been a slowdown in the rate of vaccination, particularly among younger people and that’s a way to encourage take-up.”
It also coincides with all adults aged 18 and over being offered both Covid jabs by the end of September.
Sean Doyle, BA’s chief executive, said on Tuesday that the traffic light system was “not fit for purpose”.
“It needs to be simplified. It needs to be adapted in the same way that we see in Europe and in the US,” he said.