The government says the deportation strategy is aimed at undermining people-smuggling networks and stemming the flow of migrants risking their lives by crossing the English Channel in small boats from Europe.
Initially, some 37 individuals were scheduled to be removed on the first flight to Rwanda, but the number has dwindled in the face of legal challenges. Newspapers reported that only a handful might now be on board.
The government has not provided details of those selected for deportation, but charities say they include people fleeing Afghanistan and Syria.
Prime Minister Boris Johnson is determined to press ahead with the policy despite the legal challenges and opposition, reportedly including from Prince Charles, the heir to the British throne.
"It's very important that the criminal gangs who are putting people's lives at risk in the Channel, understand that their business model is going to be broken and is being broken by this government," Johnson told LBC radio.
"They are selling people false hope and luring them into something that is extremely risky and criminal."
The Court of Appeal will hear arguments from two human rights groups and a trade union on Monday after a judge refused their request for an injunction blocking the flight taking off.
The judge said last week there was a "material public interest" in allowing the government to pursue the policy.
The High Court will separately hear arguments from Asylum Aid, a refugee charity, which launched a second legal challenge to stop the government flying refugees to Rwanda.
The charity said the government's plan to give asylum seekers seven days to obtain legal advice and to present their case to avoid deportation is flawed and unfair.
This case will be heard by the same judge who on Friday rejected the first request for an injunction.
Human rights group say the policy is inhumane and will put migrants at risk. The UNHCR has said Rwanda, whose own human rights record is under scrutimy, does not have the capacity to process the claims.
Over the weekend, Prince Charles was reported by The Times newspaper to have privately described the government's policy as "appalling". A spokesperson for Charles did not deny he had expressed personal opinions about the policy but said he remains "politically neutral".
Under Britain's unwritten constitution, the royal family are expected to avoid making political comments.