Fake notes were put in the sun "to dry" during a protest in front of a HSBC branch building.
The New York Times reported Saturday.
Citing unnamed federal authorities with direct knowledge of the investigations, the newspaper said the investigators were also probing whether HSBC circumvented US law by transferring money through its American subsidiary for sanctioned nations, including Iran, Sudan and North Korea.
Last month, HSBC announced that its Mexico unit had paid a fine totalling $27.5-million to Mexico's banking regulators for breaching anti-money laundering controls.
Earlier, HSBC apologised and a senior executive resigned after US lawmakers accused Europe's biggest bank of giving Iran, terrorists and drug dealers access to America's financial system.
In a 330-page report, the US Senate found the lender allowed affiliates in countries such as Mexico, Saudi Arabia and Bangladesh to move billions of dollars in suspect funds into the United States without adequate controls.
The report said HSBC's Mexican affiliate "transported $7.0 billion in physical US dollars to HBUS from 2007 to 2008… raising red flags that the volume of dollars included proceeds from illegal drug sales in the United States."
According to The Times, eager to resolve the investigation, HSBC reached out to federal prosecutors in July in hopes of securing a settlement by September.
But officials said a settlement in the next couple of weeks was highly unlikely, the paper pointed out. – Sapa-AFP