A report by US website Politico suggested that Americans who wanted to avoid taxes preferred other places, like Bermuda, the Cayman Islands or Singapore, and not Panama.
These countries speak English, operate under a derivative of English common law and have political systems seen as more stable, it said.
"If there was a leak from Singapore, as opposed to Panama, which is what we have so far, we might find more [evasion]," Reuven Avi-Yonah, a law professor at the University of Michigan, told Politico.
He said estimates of the annual costs of illegal tax evasion for the US ranged from $20bn (£14bn) to $70bn.
However, Mr Sharp said US laws like the Foreign Account Tax Compliance Act (FATCA) and other cross-border initiatives had meant that the "tax evasion game [was] principally over for American taxpayers".
"The list of known countries used by Americans to evade taxes is growing shorter as the day grows longer," he said.
