Weltwoche magazine on Thursday revealed the investigation against Hildebrand, 50, who was forced to step down over a scandal involving currency trading by his wife in August and September 2011.
Asset management firm Black Rock, Hildebrand's current employer, said he denies the allegations relating to potential violations of secrecy laws.
Black Rock spokesman Marc Bubeck told Reuters in an email that the allegations involve a "complaint regarding violation of federal secrecy law brought by a private person in July 2012."
Hildebrand's wife, Kashya Hildebrand, a former currency trader and Zurich art gallery owner, made a 75,000-franc profit when she purchased $504,000 and resold it three weeks later after the franc lost value following an intervention by the central bank.
Philipp Hildebrand has denied insider trading although he admitted to making a mistake by not cancelling the trade when he became aware of it because it was on the couple’s joint account.
He stepped down when public pressure mounted over the trade which was allegedly disclosed by a bank whistleblower, who has since been fired and charged with violating banking secrecy laws.
The whistleblower allegedly passed on the information to Christoph Blocher, a billionaire industrialist and vice-president of the right-wing Swiss People’s Party, who was a vocal critic of Hildebrand’s policies at the SNB.
The federal prosecutor’s office confirmed on Thursday that a legal procedure was opened against Hildebrand following a complaint filed in Zurich, AFP reported.
But the office did disclose any additional information.
Hildebrand is currently based in London as vice-chairman of Black Rock, which bills itself as the world’s largest asset management firm, headquartered in New York.