Dominic Raab said the government “will consider” introducing mandatory hotel quarantines for international arrivals in response to new strains of COVID found in South Africa and Brazil.
The foreign secretary was asked on Sunday about reports in The Sunday Times that travellers would be subject to New Zealand-style rules which would require them to pay to stay at an airport hotel for two weeks.
According to the newspaper, officials would then use GPS and facial-recognition technology to check that people are staying in their accommodation.
Asked whether hotel quarantines for international arrivals would be introduced Raab told Sky's Sophy Ridge on Sunday: "We will consider all the measures in the round.
"In terms of enforcement, we are going to be strengthening the checks at the border - so when people come in - to make sure that they have filled out the passenger location form, that they have got that negative test that they have to vouch for before they get on the flight.
"Also, because the effect of abolishing or suspending the travel corridors is that people go into quarantine and self-isolation for 10 days, we're making sure that Public Health England checks are in place to make sure people are adhering to those rules.
"As well as changing the rules, we are also making sure that we beef up the capacity to make those checks."
It comes after travel to the UK from Brazil, Portugal and 14 other countries has been banned in response to a new strain of COVID originating in Brazil.
Experts have warned that the new variant could be more infectious than the strain from South Africa - which is also on the UK’s list of countries under a travel embargo.
Watch: Minister insists UK travel rules are ‘robust’
Raab dismissed claims that the government had been "too slow" in setting up border measures to prevent the importation of new coronavirus variants.
He told the BBC’s Andrew Marr programme: "I don't accept that we have been too slow in this - we are broadly the same pace in terms of Canada and Germany."
Raab added that people should not go on holiday as he warned that the NHS is "on the cusp".
"I think right now people should be staying at home unless it is absolutely necessary, so, no, they shouldn't be going on holiday - I don't think that is appropriate," he told Sky.
"Any travel, domestic or otherwise, ought to be for the limited exceptions that have been spelled out.
"We've got this narrow period where the NHS is on the cusp, we've got to protect it, and we've got the light at the end of the tunnel with the vaccine rollout.”