A preliminary finding by the European Commission has found that Ireland provided potentially illegal state aid to tech giant Apple for more than 20 years.
It said it has doubts that two "sweetheart" tax deals agreed in 1991 and 2007 between Apple and Ireland are compatible with the internal market of the European Union.
In a statement, the European Commission said: "Accordingly, the commission is of the opinion that through those rulings the Irish authorities confer an advantage on Apple.
"That advantage is obtained every year and ongoing.
"At this stage, the commission has no indication that the contested measure can be considered compatible with the internal market".
It added: "The commission's preliminary view is that the tax ruling of 1991 and of 2007 in favour of the Apple group constitute state aid."
The Irish government has already responded and said: "As this is an ongoing legal process, Ireland will not be commenting further on any individual aspects of this case."
Apple has had a base in Ireland since 1980 and has expanded in recent years, while authorities in Brussels have powers under state aid rules to impose large fines.
The commission can fine companies up to 10% of turnover and the ability to fine Ireland up to €1bn (£780m).
The inquiry found that in effect Apple ensured it had greater profitability in the areas in which their tax charge would be the most modest.
Baker Tilly senior tax partner George Bull told Sky News if the EU findings are upheld, Apple's tax liability may be recoverable from 2003 onwards.
According to reports, US-based Apple has built up an offshore cash pile of $137.7bn (£84.8bn) in Ireland.
The money cannot be repatriated to the US without being taxed, and instead the company has sought to buy back some shares held by investors.
Apple has denied any wrongdoing over tax rulings agreed with Irish officials in 1991 and 2007.
In a statement Apple said: "Apple has received no selective treatment from Irish officials over the years.
"We're subject to the same tax laws as the countless other companies who do business in Ireland.
"To continue that growth and the benefits it brings to the communities where we work and live, we believe comprehensive corporate tax reform is badly needed."
The commission is also investigating arrangements between coffee chain Starbucks and the Netherlands, and any deal between Luxembourg and car company Fiat.
On Monday, Chancellor George Osborne warned tech firms "that go to extraordinary lengths" to cut their UK tax bills will be hit with new anti-avoidance legislation.
He hinted of plans to raise "hundreds of millions" in revenue from the likes of Microsoft, Google and Twitter.