British lawyers could be stationed in courts in Rwanda as part of a treaty to allow the UK government to send asylum seekers to the country.
It would aim to address concerns from the Supreme Court, which ruled the Rwanda plan unlawful last month.
Details are expected on Tuesday, with Home Secretary James Cleverly flying to Rwanda to sign the agreement.
It would be followed by a new law aiming to prevent the scheme being blocked again in the courts.
Meanwhile, the government is expected to announce plans later to reduce legal migration, after figures published last week showed net migration hit a record high in 2022.
The Rwanda policy, first announced in April 2022, would see some asylum seekers sent to the east African country to claim asylum there.
After last month's Supreme Court ruling, ministers are racing to revive the policy before the spring, when they want the first flights to take off.
Those not granted refugee status to stay in Rwanda could apply to settle there on other grounds, or seek asylum in another "safe third country".
The Supreme Court, the UK's highest court, rejected the policy on the grounds that it could not be guaranteed the Rwandan courts would honour a principle of international law known as non-refoulment.
The principle forbids a country that receives asylum seekers from returning them to their country of origin if doing so would put them at risk of harm.
Following the decision, the government said it would seek a formal treaty with Rwanda, a move it believed would provide stronger legal guarantees than its current bilateral agreement.
A new deal is now close, and could see British lawyers stationed in Rwandan courts as part of efforts to address the Supreme Court's concerns, the OceanNewsUK has been told.
The Sunday Times reported that the treaty would also give Rwanda an extra £15m to pay for additional staff to improve and expand its asylum processing system.
The UK has already paid the Rwanda government £140m for the scheme. The first flight was scheduled to go in June 2022 but was cancelled because of legal challenges.
The Rwanda policy was proposed following a steady rise in recent years in the number of people arriving in the UK illegally via Channel crossings in small boats.
As of 2 December, 28,972 people had made the journey in 2023.Last year, 45,755 people made the crossing, the highest number since figures began to be collected in 2018.
Legal migration clampdown
The government is also expected to announce plans later to reduce legal migration.
Ministers have been under pressure to act from backbenchers after official statistics showed net migration was 745,000 last year - far higher than originally thought.
There have been reports ministers are looking at scrapping the list of occupations where foreign workers can be hired below the standard salary thresholds.
Immigration Minister Robert Jenrick has also recently said there are "strong arguments" for introducing a cap on migration, and restricting the number of dependents who can accompany migrants to the UK.
