Ministers will discuss at a meeting on Monday whether to tighten restrictions at UK borders – including the possibility of hotel quarantines for travellers, the BBC has been told.
At a Downing Street news conference on Friday, Prime Minister Boris Johnson did not rule out taking further action.
It comes amid increased concerns over the spread of new coronavirus variants.
Under current travel curbs, almost all people arriving in the UK must test negative for Covid to be allowed entry.
The test must be taken in the 72 hours before travelling and anyone arriving without one faces a fine of up to £500.
All passengers are also required to quarantine for up to 10 days, although the isolation period can be cut short with a second negative test after five days in England.
The only people not subject to the conditions are children under 11, hauliers, air, international rail and maritime crew, and passengers from the Common Travel Area – comprised of the Republic of Ireland, the Channel Islands or the Isle of Man