Senior government ministers will meet on Tuesday to consider the plan, which would see arrivals into the country sent to designated COVID hotels to ensure they follow self-isolation rules.
The proposal is said to have the backing of health secretary Matt Hancock, chancellor Rishi Sunak, home secretary Priti Patel and cabinet office minister Michael Gove.
The move is being considered after the emergence of new variants of coronavirus in Brazil and South Africa, which scientists fear may be less susceptible to existing vaccines.
On Sunday, Hancock said there were 77 known cases of the South African variant in the UK and nine of the Brazilian strain. He said all the cases of the South African variant were linked to travel.
“The new variant I really worry about is the one that is out there that hasn’t been spotted,” he said.
Watch: What you can and can’t do during England’s lockdown