The government considered building an asylum processing centre on Ascension Island, a UK territory in the Atlantic.
Home Secretary Priti Patel asked officials to look at asylum policies which had been successful in other countries, the BBC has been told.
And the Financial Times says Ascension Island was suggested as an outpost to process applications.
A source said ministers were looking at “every option that can stop small boat crossings and fix the asylum system”.
The idea of “offshoring” is being looked at, but sources said finding an appropriate location would be key.
“The UK has a long and proud history of offering refuge to those who need protection. Tens of thousands of people have rebuilt their lives in the UK and we will continue to provide safe and legal routes in the future.
“As ministers have said we are developing plans to reform policies and laws around illegal migration and asylum to ensure we are able to provide protection to those who need it, while preventing abuse of the system and the criminality associated with it.”
No final decisions have been made.
Labour’s shadow home secretary Nick Thomas-Symonds said: “This ludicrous idea is inhumane, completely impractical and wildly expensive - so it seems entirely plausible this Tory government came up with it.”
In order to be eligible for asylum in the UK, applicants must prove they cannot return to their home country because they fear persecution due to their race, religion, nationality, political opinion, gender identity or sexual orientation.
Asylum seekers cannot work while their claims are being processed, so the government offers them a daily allowance of just over £5 and accommodation, often in hostels or shared flats.
Delays in processing UK asylum applications increased significantly last year with four out of five applicants in the last three months of 2019 waiting six months or more for their cases to be processed, compared with three in four during the same period in 2018.
In Australia, asylum seekers can be sent to an offshore processing centre while their claims are processed. Currently Australia has centres on the Pacific island nation of Nauru and another on Manus Island in Papua New Guinea.
Ascension Island, which is a British territory about 5,000 miles from the UK, has a population of fewer than 1,000.