The number of asylum seekers due to be removed from the UK on the first deportation flight to Rwanda is close to single figures, sources say.
The Court of Appeal is set to decide later whether to allow the Home Office flight to depart on Tuesday.
Campaigners and migrants last week against the government policy in the High Court.
But it is thought the number facing being deported to Rwanda's capital Kigali is falling rapidly.
A Home Office source told the BBC that, of the original 37 scheduled to fly to the east African nation, legal challenges relating to modern slavery and human rights claims have drastically reduced that number.
And BBC home editor Mark Easton says it is expected that could be "whittled down to zero" before the plane is due to take off.
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As of Friday, up to 130 people had been notified they could be removed.
The UK says sending some asylum seekers who arrive illegally in the UK to Rwanda .
The appeal to the Home Office's policy has been brought by Public and Commercial Services Union (PCS), who represent 80% of Border Force staff, along with the charities Care4Calais and Detention Action.
A separate case is also due to be heard in the High Court on Monday, after another refugee charity, Asylum Aid, applied for an urgent interim injunction against the flights to the east African nation.
The Rwanda policy has been criticised by charities, religious leaders, opposition parties - and reportedly by the Prince of Wales, who privately described it as "appalling", according to the Times.
Rwanda's high commissioner to the UK Johnston Busingye told the his country would be a "safe haven" for migrants.
Home Secretary Priti Patel says the "vast majority" of those who arrive via illegal routes - such as unauthorised boats and stowing away in lorries - will be considered for relocation to Rwanda.
But it is understood that those prioritised under the scheme will be adults, with officials insisting families arriving in the UK will not be split up.
Iranian ex-policeman fears being killed if sent to Rwanda
Among the people informed they will be sent to Rwanda on Tuesday is an Iranian ex-police commander who fled the country after refusing to shoot protesters during anti-government demonstrations in 2019.
The former commander, who is not being named in order to protect his identity, was sentenced by an Iranian military court to almost five years in jail in Iran and fears being killed by Iranian agents if he is deported.
The man previously gave testimony to the UK-based Aban Tribunal investigating alleged Iranian atrocities during the unrest, which estimates say led to the deaths of between 300 and 1,500 people.
He has been held at Brook House detention centre near Gatwick Airport after arriving in the UK from Turkey in May, where he had been in hiding for over a year after fleeing Iran.
Last week the former commander was given malaria pills in preparation for his trip, but he refused to take them and claims to have told the officers: "You can only send my dead body to Rwanda".