Apple boss Tim Cook stressed at the time that the company paid the tax it owed.
"US multinational firms are the global grandmasters of tax avoidance schemes that deplete not just USA tax collection but the tax collection of most every large economy in the world", former corporate tax adviser Edward Kleinbard was quoted as saying by the NYT.
Apple said that reforming the worldwide tax system to make it simpler is "essential" and needed to "remove the current tug of war between countries over tax payments".
Although it was aimed at Double Irish structures, the potential rule change would ban all Irish companies from claiming tax residency in a tax haven.
Apple moved the tax home of two Irish subsidiaries to Jersey, a self-governing island in the English Channel between Britain and France, and also made Ireland the tax home of a different European subsidiary.
A trove of documents known as the Paradise Papers have reportedly shed light on Apple's search for a new place to store the huge sums, after more than two decades of benefiting from artificially low taxes in Ireland.
Vestager also said it was too early to say whether the latest leaks on tax arrangements by companies would lead to any general investigations.
The majority of the leaked Paradise Papers come from Appleby, which specialises in offshore accounts.
The company said that it told regulators in the US and European Commission of the reorganization of its Irish subsidiaries in 2015 and said the moves did not reduce its tax payments in any country.
- Britain's Queen Elizabeth II has, through the Duchy of Lancaster which provides her income and handles her investments, placed around £10 million ($13 million, €11.3 million) of her private money in funds held in the Cayman Islands and Bermuda. Apple's offshore profits aren't taxed by the U.S. and they're largely untouched by other governments.
A law professor who reviewed the documents told the newspaper that there was a "strong possibility" that Apple moved intellectual property to Ireland in a transfer worth almost $200 billion. It said the move was made "specifically to ensure that tax obligations and payments to the USA were not reduced".
"We believe every company has a responsibility to pay the taxes they owe and we're proud of the economic contributions we make to the countries and communities where we do business".
"Additional tax is then also due in the United States when the earnings are repatriated", the statement said.
As Apple came under pressure in the USA and Europe about what was called the "double Irish" scheme, it enlisted offshore finance law firm Appleby to find a new place to stash cash out of the reach of tax collectors, reports said. The company reports its effective global tax rate at 24.6 percent.