US Attorney General Eric Holder warned that no financial institution should consider itself "above the law," amid investigations into alleged tax evasion and money laundering by European banks.
A senior US official told AFP on condition of anonymity that probes of BNP Paribas and Credit Suisse are almost completed and criminal charges could be brought within "a few weeks."
And the Wall Street Journal reported that Credit Suisse was about to reach an agreement with the Justice Department that would see it plead guilty to helping wealthy Americans evade taxes by sheltering their funds abroad, and pay a $1 billion fine.
Credit Suisse fell more than 2.3 percent on the Swiss Exchange on Monday.
Its Swiss rival UBS paid US authorities $780 million in 2009.
BNP Paribas is under investigation over allegations of money laundering and breaching US financial sanctions against certain third parties, the senior US official said.
"There is no such thing as 'too big to jail,'" Holder said.
The top US law enforcement official did not cite the French and Swiss banking giants by name, but his weekly audio message warned that the Justice Department would "follow the facts wherever they lead."
US law enforcement and regulatory authorities have been criticized since the financial crisis of 2008 for not bringing criminal charges against some institutions and individuals accused of fraud.
But Holder, whose department oversees the FBI and its financial crimes task force, denied that the United States was unwilling to prosecute the pillars of the international banking system.
He rejected "the theory that certain financial institutions... should be considered immune from prosecution due to their sheer size and their influence on the economy."
And he insisted: "To be clear: no individual or company, no matter how large or how profitable, is above the law."
"When laws indeed appear to have been broken -- and the evidence supports the allegations -- a company's size will never be a shield from prosecution or penalty," Holder added.
"I intend to reaffirm the principle that no individual, no entity that does harm to our economy is ever above the law."
Holder said he was personally monitoring the status of the investigations and was dedicated to seeing them completed.
The probe carried out by the Justice Department, the Treasury and financial services regulators in New York must determine if BNP, as well as French banks Credit Agricole and Societe Generale, laundered money and broke US embargoes by doing business with countries such as Cuba and Iran, a source close to the investigation said.
The Journal said BNP Paribas is in talks with US authorities to reach an out of court settlement.