Labour has branded Priti Patel's plan to send asylum seekers to offshore immigration centres for processing as "unconscionable" and said it will oppose the policy.
The Home Secretary has reportedly opened talks with Denmark, whose government has already passed legislation to pursue a similar policy and open a processing centre outside Europe.
The Times newspaper reports that the UK and Denmark could potentially set up a shared centre in Rwanda, a landlocked country in central Africa.
Describing the policy as "unconscionable", shadow home secretary Nick Thomas-Symonds said on Sunday night Labour would oppose the proposals.
The idea of processing applicants for refugee status offshore has been a perennial suggestion of Home Secretaries going back decades, and has also repeatedly been discussed at an EU level in various forms without agreement.
The approach is attractive to ministers who want to circumvent the UK's international obligations to refugees, and who would like to appear "tough" against people arriving in the UK.
The Home office also claims the policy will deter people from travelling to the UK.
However, previous attempts to make the policy work have always failed to get off the ground.
The Nationality and Borders Bill, to be introduced to the Commons next week, will include a provision to create an offshore immigration processing centre.
The approach requires the cooperation of a third country willing to host any offshore centre.
A similar approach has been followed in Australia since 2012, with migrants arriving in the country sent to detention camps in Nauru and Papua New Guinea. Human rights groups say the policy is rife with rights violations.
Domestic immigration detention facilities in the UK have also been rife with abuse and poor treatment and some campaigners say they should be closed.
Labour's Mr Thomas-Symonds said: "These same plans have been mooted before. They are unconscionable. Labour will stand against them."
A Home Office spokesperson said: "Our asylum system is broken and we cannot sit idly by while people die attempting to cross the Channel. Our New Plan for Immigration will welcome people through safe and legal routes, whilst preventing abuse of the system and the criminality associated with it.
"People should claim asylum in the first safe country they arrive and we must ensure dangerous journeys are not incentivised.
"We have been looking at what other countries do to deter illegal migration and this work continues. We will not rule out any option that could help reduce the illegal migration and relieve the pressure on the broken asylum system."
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