The agreement was part of a $1.9 billion settlement that allowed HSBC to avoid criminal charges after it was found to have helped move hundreds of millions of dollars in illicit drug money through the U.S. financial system.
"It is quite possible that the (agreement) may be reopened as a result of the bank's activities on either or both the tax evasion and foreign exchange manipulation front," said the U.S. law enforcement official, who requested anonymity because the investigations are ongoing.
British lawmakers said they plan to open an inquiry into the bank after it came under fire for its past practices in Switzerland.
Read MoreLawmaker: HSBC 'asleep' or complicit in tax scheme
HSBC shares fell 2 percent by 0845 GMT (3.45 a.m. EST) on Tuesday, underperforming the European bank index. They fell 1.6 percent on Monday after media reports about the activities of its Swiss operation based on client data from 2006-07.
A spokesman for HSBC declined further comment on Tuesday after the bank issued a statement late on Sunday in response to the media reports.
The International Consortium of Investigative Journalists (ICIJ), which coordinated the release of details of leaked client data, said a list of people who held HSBC accounts in Switzerland included soccer and tennis players, rock stars and Hollywood actors.
Reuters could not independently verify any of the names listed by the ICIJ. Having a Swiss bank account is not illegal and many are held for legitimate purposes.
The newly released HSBC Swiss client list included royalty such as Morocco's King Mohammed, politicians, corporate executives including former Santander chairman Emilio Botin, who died last year, and wealthy families, the ICIJ said. A spokesman for the Moroccan royal palace declined to comment.
Uruguayan soccer player Diego Forlan, who was also on the list, on Monday denied evading taxes by hiding money in Swiss accounts with HSBC.
The documents also listed arms dealers, people linked to former dictators and traffickers in blood diamonds, and several individuals on the current U.S. sanctions list, including Gennady Timchenko, an associate of Russian President Vladimir Putin. Timchenko's Volga Group declined to comment.
"We acknowledge and are accountable for past compliance and control failures," HSBC said after news outlets published the allegations about its Swiss private bank.