Priti Patel has been urged to drop "dystopian" plans to send asylum seekers to a processing centre in Africa.
The Home Secretary is reportedly in talks with Denmark over a shared facility in Rwanda as the government draws up new legislation for the UK's border controls post-Brexit.
Boris Johnson is said to back the plan after the arrival in Britain this year of over 5,600 migrants, who crossed the Channel in small boats.
It comes after the government failed to strike a deal with France and other EU states over migration.
Danish ministers are said to have visited Rwanda, a Commonwealth country, to sign a memorandum last month ahead of passing new laws.
It is said UK ministers believe the plan could break up people-trafficking criminal gangs who make huge sums from refugees.
But the plan is expected to face a fierce backlash from charities and opposition MPs.
Enver Solomon, chief executive of the Refugee Council, said: "For generations, men, women and children seeking protection in the UK have been given a fair hearing on British soil.
"Most have rebuilt their lives as law-abiding citizens making a huge contribution to our communities.
"Offshore processing is an act of cruel and brutal hostility towards vulnerable people who through no fault of their own have had to flee war, oppression and terror."
The Lib Dems called the proposals "appalling and inhumane".
“The UK has a proud history of providing sanctuary and support to those in need, but now Priti Patel and the Conservatives are turning their backs on refugees who are seeking safety," said the party's home affairs spokesman, Alistair Carmichael.
“Treating seekers of sanctuary as criminals is wrong and will only strengthen the position of people smugglers and human traffickers who prey on desperate people trying to cross the Channel."
The Prime Minister's official spokesman denied any talks with the Danish government were underway but would not rule out using a centre in Rwanda, telling reporters: "We are working with our international partners to meet the challenge posed by our current asylum system, which is fundamentally broken [and] which we need to make fair but firm."
A government source told the Times the numbers of asylum seekers making it to Britain was having a "political impact" for Mr Johnson.
They said: "The Prime Minister and Home Secretary are determined to look at anything that will make a difference on Channel crossings.
"The numbers have a psychological and political impact that goes far beyond the actual numbers involved.
"The idea that people are coming in at will - even if it is a relatively small proportion of immigration to the UK - doesn't give the impression we are in control, especially when young people are washing up in dinghies.
"The only way to really tackle this problem is to tackle the pull factors, which is what the ideas around offshore processing and the presumption that if you cross illegally then your asylum applications are going to be treated less favourably than legal routes are about."
