Parliament will resume voting on the government's controversial Rwanda bill on Monday as MPs return to the Commons.
It comes as reports suggest the UK held talks with other countries, including Armenia, about replicating the scheme.
The plan to send some asylum seekers to Rwanda has faced setbacks since it was first announced in April 2022.
But legislation to declare Rwanda safe is likely to pass this week - with the government majority meaning amendments made by peers should be overturned.
As reported in the Times, internal government documents show Costa Rica, Ivory Coast and Armenia have been considered as options for similar schemes, if Rwanda proves successful.
The BBC has seen some of the documents, which are from several months ago, and understands the list is accurate.
The early stage plans are described by sources as in a "holding pattern", with other countries keen to see if the Rwanda plan actually gets going before trying anything similar themselves.
Other African nations, including Morocco, Tunisia, Namibia and Gambia, "explicitly declined" to enter technical discussions, according to the Times.
A government spokesperson said the UK "is continuing to work with a range of international partners to tackle global illegal migration challenges" but its current focus was on passing the Rwanda bill and putting plans in place to get flights off the ground as soon as possible.
Labour believes the scheme is flawed and intends to scrap it if it wins the general election, expected to be held later this year.
Sir Keir Starmer has said he would instead focus on targeting criminal gangs and negotiating new security arrangements with Europe.
Meanwhile, charities supporting asylum seekers are also planning to launch legal challenges "as quickly as possible" against deporting people to the east-central African country if the bill becomes law this week.
The government will be seeking to strip out changes made by the House of Lords - which sent the bill back to the Commons with additional provisions including the need to ensure "due regard" for domestic and international law.
Other proposed changes include exemptions from deportation for victims of modern slavery and those who have supported UK armed forces overseas.
In response the government will instead promise to publish an annual report about the operation of the legislation and how it relates to provisions in the treaty with Rwanda to ensure it takes all necessary steps to accommodate the needs of victims of modern slavery.
Labour peer Baroness Chakrabarti said the Lords amendments sought to improve the bill and did not attack "the central plank of the policy".
She told BBC Radio 4's Today programme her own amendment would restore "the jurisdiction of domestic courts, who are defenestrated by this bill".
However, Conservative MP Sir John Hayes said legal appeals had been used to block deportations and "frustrate" the will of Parliament and government policy.
Prime Minister Rishi Sunak has repeatedly said flights to Rwanda would take off by spring, but refused to name a specific date.
Ministers believe the legislation will pave the way for the first removals to the country within weeks.
The Safety of Rwanda Bill declares the country safe and was introduced to Parliament after the Supreme Court ruled unanimously that the government's scheme was unlawful.
In its ruling, the court said genuine refugees being deported there would be at risk of being returned to their home countries, where they could face harm.
The Rwanda scheme was originally introduced by then-Prime Minister Boris Johnson in April 2022 with the aim of acting as a deterrent to people from arriving in the UK on small boats across the English Channel.
It has faced a number of legal challenges since, and so far no-one has been sent to the east African country under the scheme.
The bill aims to protect the scheme from further legal setbacks.
It comes as 534 migrants crossed the Channel in 10 boats on Sunday - the highest daily figure this year.
It brings the total for 2024 so far to 6,265, an increase of 28% on the same period last year.
