Under US securities rules, a material event is usually defined as 5 per cent of a company's average pre-tax earnings for the past three years. For Apple, which reported the highest quarterly profit ever for a US company in January, that could exceed $2.5bn, according to FT calculations.

The warning came in Apple's regular 10-Q filing to the Securities and Exchange Commission on Tuesday, a day after it reported first-quarter revenues of $58bn and net income of $13.6bn.

Brussels has the power to order Dublin to reclaim 10 years of tax advantages granted to Apple if it finds that deals struck in 1991 and 2007 were unlawful.

Both the Irish government and Apple have consistently denied any wrongdoing and declined to comment on the size of any fine. However, some Brussels officials suggest any ruling could set a new record for a state-aid investigation penalty by comfortably topping €1bn.