With the prime minister under huge pressure to get on top of illegal arrivals, official figures to be published on Thursday are expected to show net migration has surged to unprecedented levels.
Mr Sunak’s government is said to be ready to cut the number of relatives foreign health and social care workers are allowed to bring with them to only one.
Tory ministers are also reportedly considering ditching the shortage occupation list, thus making it more difficult for British employers to bring in overseas staff to fill gaps.
A move to raise the minimum salary requirement for foreign worker visas from £26,200 to about £31,000 could also be brought in more quickly than planned.
No 10 said it was examining options to cut net migration levels. Mr Sunak’s spokesperson said: “This is something that we are actively looking at.”
Increasing the minimum salary threshold for foreign workers could be announced as soon as Thursday, according to The Times.
The newspaper reported that the Home Office, under the former home secretary Suella Braverman, had been pushing for a ban on foreign health and care workers’ bringing dependants, despite objection from the Department of Health and Social Care (DHSC).
But No 10 is thought to be keen on a compromise by restricting the number of dependents to one on health workers’ visas.
Madeleine Sumption of the Migration Observatory at Oxford University said the shortage occupation list is “bringing people into really low-paid jobs”.
She added: “If the salary threshold was much higher, that wouldn’t be the case anymore and there might be more of an argument for [it].”
Net migration hit a record high of around 606,000 last year. But this week’s figures from the Office for National Statistics are expected to show a new milestone of 700,000.
Meanwhile, Mr Sunak is under pressure from his own MPs to set out a workable, revised “plan B” to send asylum seekers arriving on small boats to Rwanda.
The prime minister will soon publish a new updated agreement with Rwanda in a bid to address the court’s concerns around “refoulement” – the potential for refugees rejected by the central African country to be sent back to the country they are fleeing.
The Tory leader will also try to come up with emergency legislation that he says will enable parliament to “unequivocally” declare Rwanda a safe destination for asylum seekers.
A leading lawyer told parliament earlier this week that the planned new treaty with Rwanda would be a “historically worthless piece of paper”.
Lord Carlile argued that Rwanda had been found to be unsafe “on the facts” by the Supreme Court. “Why doesn’t the government see that the proposal of a treaty with Rwanda would produce a document which would be yet another historically worthless piece of paper?”
The former Supreme Court judge Lord Sumption has said the Rwanda plan is “probably dead”. He said it would be “constitutionally extraordinary” for the prime minister to “change the facts by law” by declaring Rwanda safe.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies