The Sunday Times newspaper said that from November, a pilot scheme would target visitors from those three countries plus Bangladesh, Sri Lanka and Ghana.
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Visitors aged 18 and over would be forced to hand over £3,000 ($4,600, 3,500 euros) from November for a six-month visit visa.
They will forfeit the money if they overstay in Britain after their visa has expired.
Initially the scheme will target hundreds of visitors, but the plan is to extend it to several thousand, according to the broadsheet's front-page report.
The weekly paper said the move by Home Secretary Theresa May is designed to show that Prime Minister David Cameron's Conservative Party is serious about cutting immigration and abuses of the system.
The populist United Kingdom Independence Party has been encroaching on the Conservatives' traditional core vote in recent months.
Cameron wants annual net migration down below 100,000 by 2015.
"This is the next step in making sure our immigration system is more s