The rules would not be applied retrospectively and children would not be subject to the payments.
"Receiving asylum support is a right, but it is also a responsibility," Home Secretary Shabana Mahmood said. "Once people can contribute and repay the generosity of the British people, we expect them to do so."
Mahmood explained that her latest reforms aim to reduce the burden on taxpayers' wallets.
The Home Office also said over the weekend that it aims to remove 45,000 more people with no legal right to remain and foreign criminals within the next decade, in addition to the tens of thousands already being removed on a yearly basis.
The center-left Labour Party has increased efforts to curb both legal and illegal immigration as it seeks to counter the rising popularity of Nigel Farage's Reform UK party, which has vowed to deport up to 600,000 asylum seekers and other people whose claims or appeals have failed.
"Mass migration has changed this country, certainly in many of our cities, literally beyond recognition," Farage told Fox News Digital last week. "We’ve not been selective about who’s been able to come into the country. That is a major contributory factor."
Refugee advocates and migration researchers have criticized the proposal, arguing it could punish people who fled persecution and questioning whether many refugees would earn enough to repay the proposed sum. Critics have also warned that tying repayment to settlement could create uncertainty for people trying to rebuild their lives in the UK.
The Labour Party has faced internal divisions over how tight its immigration policy should be, and the party is up against further overall uncertainty after its leader, Prime Minister Keir Starmer, announced last week that he will resign.
Reuters contributed to this report.