Italian magazine L'Espresso reported that Jean-Baptiste de Franssu's son works for Promontory Financial Group, which is conducting a forensic investgation into the bank and its client relationships.
Louis-Victor Douville works as a London-based analyst for the US company, according to its website.
"The question of a conflict of interest is not an issue for us because, by law, the AIF (the Vatican's financial watchdog), has approved the appointment of our president," bank spokesman Max Hohenberg told AFP.
Allegations of money laundering have dogged the bank for decades, most famously in the early 1980s when it was the main shareholder of the Banco Ambrosiano, which collapsed in amid accusations of links with the Sicilian Mafia.
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More recently the bank has been investigated for money laundering by Italian authorities, with its director general and his deputy placed under investigation and forced to resign last year.
According to L'Espresso, his son was hired at Promontory a few months earlier.