Deputy Prime Minister Nick Clegg announced the plans on Friday. The deposits will be repaid when the visitors leave the country, The Independent daily reported.
Although a list of such "high risk" nations has not yet been drawn up by the UK Border Agency (UKBA), it is expected to include Pakistan, other countries in the Indian sub-continent and some in the Middle East, the report said.
Clegg, who chairs the cabinet's Home Affairs Committee, has asked the Home Office to run a trial "security bonds" scheme by the end of this year.
The bonds would cost at least £ 1,000, rising to as much as several thousand pounds for visitors from the countries deemed to pose the highest risk.
"The challenge isn't just stopping people coming into Britain illegally, it's about dealing with individuals who come over legitimately but then become illegal once they're already here," Clegg said, describing the bonds as a "powerful new tool".
He, however, added that the bonds "would need to be well-targeted so that they don't unfairly discriminate against particular groups".
"The amounts would need to be proportionate, we mustn't penalise legitimate visa applicants who will struggle to get hold of the money," Clegg said.
"I would want a system that is welcomed by legitimate visitors. Rather than place a great burden on them - done right, this would speed up the application process, giving UKBA greater confidence about people's intentions, allowing them to make better, faster decisions," he said.
The daily said Clegg has asked Home Secretary Theresa May to double the maximum fine for unscrupulous employers who hire illegal migrants as cheap labour.
Clegg said he wants it to go up to £ 20,000 per illegal worker.