Other big international banks were also cited in the investigation, according to the source, who refused to confirm their names or say when the probe was launched.
"The US is investigating foreign banks for potential issues related to money laundering and violations of US embargoes and sanctions on countries like Cuba, Iran and Sudan," the source said.
The US Treasury, Justice Department, Manhattan district attorney and New York Department of Financial Services are investigating the banks.
BNP Paribas is in talks with US authorities to settle the probe, according to The Wall Street Journal.
Last month, France's largest listed bank said it had set aside $1.1 billion to cover potential penalties for transactions in countries under US sanctions.