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Details of nationality, immigration and visa status should be recorded whenever a criminal is convicted, ex-immigration minister Robert Jenrick has proposed.
Mr Jenrick plans to submit an amendment to the government's Criminal Justice Bill, saying the data would help to inform deportation and visa policies.
"We would want to apply a higher level of scrutiny to nationalities that are higher risk" he said.
Rishi Sunak has been under pressure to cut net migration figures.
Revised estimates published in November indicated net migration - the difference between the number of people arriving and leaving Britain - reached a record 745,000 in 2022.
Mr Jenrick resigned as immigration minister in December in protest at the prime minister's Rwanda deportation plan.
His proposed amendment, first reported by the Daily Telegraph, would mean a report presented to Parliament each year which would collate the nationality, visa and asylum status of every offender convicted in English and Welsh courts in the previous 12 months.
According to the Telegraph, Mr Jenrick's plan has been backed by more than a dozen Conservative MPs, including Sir Jacob Rees-Mogg and Sir Robert Buckland.
If the amendment is submitted, it could then be selected to be voted on by the entire House of Commons as the overall Bill continues its passage through Parliament, and then become part of the government policy if it is backed by a majority of MPs.
Mr Jenrick told BBC Radio 4's Today programme that in his role as immigration minister he encountered "significant and growing evidence that we [the UK] were importing crime."
He said: "In the field of drug production, the National Crime Agency have been very clear that a significant proportion of the UK's drug trade is being fuelled by Albanian drug production."
He added that this had led to him investing "a great deal of time tying to stop that".
Mr Jenrick said a risk-based strategy was already applied to visa applications.
"What I'm proposing is that this data on crime plays a part in that. We would want to apply a higher level of scrutiny to nationalities that are higher risk," he said.
Denmark and some US states apply a similar approach, he said.
Mr Jenrick said in Denmark "some nationalities are, in fact, more law-abiding than Danish citizens, but many are not and some very prominently are causes of, in the Danish example, violent crime."
Having data would enable government to "interrogate" the statistics on crime and make policy choices, he said.
"The public should be aware of the trade-off of migration," he said. "There is a prevailing orthodoxy that it is an unadulterated good. I don't think that's always the case."
Convicted criminals are already subject to visa restrictions. UK government guidelines state that any foreign national who has been convicted of a criminal offence in the UK or overseas and handed a custodial sentence of 12 months or more would "normally" be refused a visa for entry into the UK.