Grant Shapps, the Minister of Transport, said he should make sure the UK does not import coronaviruses once the infection rate starts to drop.
Reports suggest that people will be asked to isolate themselves for two weeks after arriving in the UK.
Airline groups have sounded the alarm over the proposed rule, which they say “kills” international travel.
Asked whether those arriving in the UK will be quarantined, Shapps told the BBC’s Andrew Marr Show: “I think it’s important because we are seeing the numbers go down and the rate R that we hope to decrease … that we make sure that the sacrifices in the sense of social estrangement that we ask the British people to make are matched by whoever comes to this country.
“So I’m actively looking at these issues right now so that when we have infection rates in the country under control, we don’t matter. “
Shapps also defended the decision not to conduct temperature checks or quarantine on the thousands of people who landed in the UK at the start of the epidemic.
He said the chief medical officer’s view was that closing the borders would have delayed the arrival of the virus for up to five days.
And he said that such a decision would have prevented the stranded Britons from returning home.
Even now, with more than 25,000 deaths, arriving in the UK are still not invited to quarantine.
Explanation of government action against coronaviruses
But Mr Shapps said it was because most of them are British returnees and those arriving are currently stranded.
The United Kingdom has one of the worst international rates of coronaviruses, although ministers warned that it is too early to compare Britain to other countries.
A week ago, reports revealed that travelers could be advised to quarantine for two weeks after arrival.
This would prevent holidays and business trips to the UK and deter Britons from going abroad due to restrictions on their return.
Boris Johnson will draw up a “roadmap” to ease the lockdown this week – but officials have made it clear he could strengthen in some areas while being released in others.
Shapps said Britain would not return to the “status quo”.
He told Sky Sophy Ridge on Sunday: “I don’t think we should expect us to move away from this situation we are in when we are socially moving away from where we were in February.
“It is clearly not going to happen and I don’t think anyone can imagine it for a moment.
“The most important thing is that the absolute goal of what the Prime Minister will announce later this week is that what we are doing in the future does not negate the brilliant work that people have done to get this number R below 1 – the all critical reproduction rate does not return, because this is when we would see a second peak.
“So no, I’m afraid it certainly won’t be as usual, but we want to make sure people understand where the route map is. “