In his letter to the Chancellor, Lord Hain had stated that a whistle-blower had indicated that the banks may have "inadvertently" been conduits for the corrupt proceeds of money and therefore, they should review transactions involving individuals and companies linked to the Gupta family and President Zuma.
The Guptas and their companies have not been charged with any crime in South Africa, but allegations by government and opposition politicians that they used a friendship with President Jacob Zuma to control state businesses are among many scandals that have dogged Zuma's presidency.
Explaining his reasons for asking for probes of HSBC and Standard Chartered, he says that the majority of the funds in question flowed through the UAE and Hong Kong, where the two banks have their biggest footprints. The Guptas deny any wrongdoing and they have not been convicted of any crime.
The Gupta empire which spans media, mining and consulting have been linked to a numerous leaked emails alleging graft in its dealings with South Africa's state-owned companies.
The FCA said: "The FCA is already in contact with both banks named and will consider carefully further responses received".
It's being reported that the FBI is investigating cash flows between South African Gupta-owned companies, Dubai and a company owned by Ashish and Amol in the United States.
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The FBI in the US has begun a probe into the Guptas, investigating their links with American companies.
There has been no comment from Gupta spokesman, Gary Naidoo.
HSBC declined to comment.
Lord Hain, a former Northern Ireland secretary, alleged in his letter to the chancellor that the issue was "a result of the corruption and cronyism presided over by President Zuma and close allies the Guptas".
Lord Hain told the House of Lords that as much as £400m of illict funds from South Africa may have been "transnationally" laundered, and called for the Government to ensure those funds were returned to the country's treasury.
"We are taking this very seriously because we realise the consequences of not doing so for the reputation of the City of London and the UK", said the UK Minister of State for the Department for International Development, Lord Bates.