EIM, an asset management company run by the wealthy French financier, Arpad "Arki" Busson, has been asked by the FBI to help trace the finances of al-Qaida or other terrorist groups.
A spokeswoman for the company, which has offices in Mayfair, central London, refused to comment on reports that it once managed money for the Bin Laden family, who do not have any involvement with terrorism and have disowned Osama.
EIM, founded in 1992 by Mr Busson - the partner of model Elle Macpherson and father of her son - is one of the best known names in the European hedge fund industry and invests money on behalf of high net worth individuals through a range of funds that offer above-average returns.
Since its inception it is thought to have managed assets of about £5bn on behalf of wealthy clients.
The firm does not manage hedge funds directly; it invests clients' cash in portfolios incorporating a range of hedge funds.
One British-based industry insider described EIM as "a very kosher outfit" with a number of institutional clients as well as super-rich individuals. Under European and British law, financial services companies are obliged to report any suspicion of money laundering to the national criminal intelligence service's economic crime unit.
British firms are also required to ensure that they know the identity of clients.
A senior executive at one of the City's largest investment banks admitted that many institutions with hedge fund operations were worried that they might have inadvertently handled money belonging to Bin Laden or al-Qaida.
"Can you imagine the retribution from American customers if it emerges that one of the big banks was making money for Bin Laden - even if it was a mistake?"
The FBI and the US treasury department refused to comment on whether there was an investigation under way into the hedge fund sector. But they are believed to be eager to talk to companies such as EIM which provide the links between investors and hedge fund investments.