The cabinet minister was unable to say how many of the 33,000 people identified as potentially eligible would be sent to Rwanda if flights begin.
Mr Cleverly told MPs the home affairs select committee the total number of deportations was “uncapped” – but said it could also be small if other work to reduce small boat crossings is successful.
It comes as the Archbishop of Canterbury and Baroness Hale – the judge who declared Boris Johnson’s Brexit-related prorogation of parliament illegal – have joined forces to thwart Mr Sunak’s current Rwanda plan.
Lady Hale has tabled a new amendment in the Lords that could derail the bill by insist that the UN High Commission for Refugees (UNHCR) declares Rwanda safe before flights can begin.
No migrants who make unauthorised crossings have been removed because of the legal challenges that resulted in the Supreme Court finding the scheme unlawful. The Home Office has identified 33,085 people as eligible.
Under persistent questioning over how many of those people will end up in Rwanda, Mr Cleverly insisted the scheme remains “uncapped” but said he could not “speculate” about the figure.
“The answer is entirely dependent on other work we’re doing in parallel,” the home secretary told MPs during his select committee grilling on Wednesday.
“It may well be if we’re successful with returns agreements, if circumstances in other countries change, it may well be that the figure is quite low,” he said.
“It could be nearly at that figure, but the point is the number of people that we might send to Rwanda is entirely contingent on a whole set of other work that we’re doing.”
So far, the UK has paid Rwanda £240m under the PM’s plan to “stop the boats”, but ministers expect to pay an additional £50m next year.
Mr Sunak is trying to revive his deportation policy by passing legislation deeming Rwanda a safe country and ratifying a new treaty with the African country.
The Rwanda Bill is currently making its way through a House of Lords that is hostile to the scheme.
Baroness Hale – the former Supreme Court president who became well known at Westminster for wearing a spider brooch during her judgement against Mr Johnson’s attempt to prorogue parliament to push through Brexit deal – has tabled a significant amendment.
It requires that the UNHCR says Rwanda is a safe country for asylum seekers before the government can send any migrants there – a move which could delay Mr Sunak’s plan.
The amendment was presented along with Church of England’s mosty senior cleric, the Rev. Justin Welby, along with leading human rights lawyer Shami Chakrabarti.
Meanwhile, Mr Cleverly also had a tussle with Labour committee chair Dame Diana Johnson over whether the 94,000 asylum claims awaiting a decision is a “backlog”.
The home secretary told her: “You keep describing it as a backlog – it’s the caseload. It’s a queue. I think your use of the word backlog implies something that I disagree with.”
“There are a number of cases that we’re working through. At any given time someone who has arrived will be added to the caseload, by your definition if someone arrived yesterday that would be a backlog,” said the Tory cabinet minister
Mr Cleverly joked that “sessions like this are a trip to the dentist, we can all pretend we enjoy it – we really don’t – but we also recognise it is quite important”.
Mr Sunak had promised to “abolish” by the end of last year the “legacy” backlog of 92,601 claims made before the end of June 2022.
The Home Office was reprimanded by the UK Statistics Authority for claiming it had been achieved when 4,537 of those applications were still outstanding.