Quarantine-free travel between Britain and some other countries could be introduced at the end of this month through so called 'air bridges'.
The Government is understood to be considering whether to enable people to travel without having to spend two weeks self-isolating on their return, depending on coronavirus infection rates remaining low enough.
Current plans mean all international arrivals - apart from people carrying out a limited number of specified roles - would need to quarantine for 14 days from Monday.
The plan has been fiercely criticised by travel and hospitality businesses, and ministers are understood to be considering introducing air bridges when the policy is reviewed three weeks after it comes into force.
Agreements would need to be reached with other countries before any policy could be introduced.
The Telegraph reported that Prime Minister Boris Johnson is "personally in favour" of the idea.
Further details of the quarantine proposal are expected to be laid before Parliament today (Tuesday).
This morning former transport minister Stephen Hammond continued to call for the plan to quarantine all people arriving from outside the UK to be scrapped.
The Tory MP told BBC Radio 4's Today programme that air bridges would be a "sensible, targeted response" between low-risk countries.
"I think the idea of air bridges are the right way forward," he added.
"I think, as we've seen across the world, people are taking measures out of the lockdown and this targeted approach would be a much more sensible way to behave."
The Guardian reported that quarantined travellers would be able to go food shopping, change accommodation and use public transport from airports.
But a Government source said people would be expected to stay in one home, use private transport and only venture outside where absolutely necessary.
