According to reports, the Home Office is planning a deportation trip to the east African country as soon as September.
The contentious policy of sending asylum seekers to the East African country has so far been stymied by judicial challenges.
Rishi Sunak is thought to be growing increasingly optimistic that the Government will prevail in the Court of Appeal against a challenge by human rights groups and unions, avoiding a Supreme Court clash.
Ministers fear that if the appeal is rejected by the courts, there will be no legal reason for pushing the matter to the UK’s top court.
“There is a world in which we are wheels-up later this year and the Supreme Court does not get involved,” a senior government source said.
Last year, the European Court of Human Rights in Strasbourg halted the first flight to Rwanda at the eleventh hour.
However, earlier this year, the High Court concluded that the system was legal.
The Court of Appeal is set to rule on the policy’s legality in the coming weeks.
It comes as the Illegal Migration Bill, a crucial component of the Prime Minister’s plan to discourage individuals from crossing the Channel in tiny boats, is presently being debated in Parliament.