The fully vaccinated individuals from the US and the EU can avoid quarantine on arrival in England.
According to the BBC, senior British cabinet ministers have been discussing loosening the restrictions for fully vaccinated individuals.
The British Foreign Secretary Dominic Raab said that a decision would be taken shortly.
Currently, people who have been fully vaccinated inside the UK do not have to quarantine when traveling from the US and EU, apart from France, because those places are on the amber list (and some EU countries are on the green list).
However, those who are vaccinated outside the UK still should abide by the quarantine restrictions.
Downing Street and the Department for Transport declined to comment on newspaper reports the government would go ahead with the plan to also exempt people vaccinated in the US and EU.
The travel industry has been pushing for this change in the rules so that people living abroad can more easily come to the UK for holidays or to visit loved ones.
"At the moment we're in this slightly ridiculous situation where if I'm on a plane from Spain, because I'm lucky enough to have had two jabs, once we get to the UK I just wander off, no problem," said travel expert Simon Calder.
"But the person sitting next to me, who happens to have had their vaccinations in Spain, not in the UK, has to go and sit in a room for 10 days. Doesn't make sense."