The Sunday Times newspaper said that from November, a pilot scheme would target visitors from those three countries plus Bangladesh, Sri Lanka and Ghana.
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.
"This is the next step in making sure our immigration system is more selective, bringing down net migration from the hundreds of thousands to the tens of thousands while still welcoming the brightest and the best to Britain," May was quoted as saying.
"In the long run we're interested in a system of bonds that deters overstaying and recovers costs if a foreign national has used our public services."
A Home Office official said the six countries highlighted were those with "the most significant risk of abuse".
Last year 296,000 people granted six-month visas were from India, 101,000 from Nigeria, 53,000 from Pakistan and 14,000 each were from Sri Lanka and Bangladesh.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.