A report in The Times newspaper suggests that some Overseas Territories could be under consideration as processing centres for asylum seekers.
The UK paper says top British government officials have named Gibraltar and the Isle of Man among several locations being looked at.
But the Chief Minister of Gibraltar, Fabian Picardo has said the issue “has not been raised with me at any level".
He told BBC News he had "very serious concerns" over the idea, which he rejected as "entirely unviable".
The Isle of Man, a British Crown Dependency, has also denied knowledge of the plan.
This comes at the British Home Secretary, Priti Patel, is preparing to introduce new legislation aimed at clamping down on refugees crossing the English Channel mainly from France.
The legislation proposes what has been described as new ‘legal safe routes for genuine refugees' to be accepted into the UK especially those coming directly from war zones.
The idea, said to be fashioned on the Australian system, surfaced last year when it was reported that the government had considered building an asylum processing centre on Ascension Island, a British Overseas Territory in the South Atlantic Ocean.
At that time, Alan Nicholls, a member of the Ascension Island Council, said moving asylum seekers more than 4,000 miles to the British overseas territory would be a "logistical nightmare" and not well received by the islanders.
In the UK, the opposition Labour Party has called the idea “ludicrous, inhumane, completely impractical and wildly expensive".
A British Home Office official has said: "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.”
The Government has sought feedback on the Digital Identity bill which is to be debated in parliament. Do you support the introduction of this Bill?