The European Commission has ordered Apple to pay the record sum after finding it paid as little as £50 on every £1m of profit.
Ireland’s finance minister Michael Noonan said he disagreed “profoundly” with the decision and would seek Cabinet approval for an appeal.
Ireland’s Cabinet are expected to meet on Wednesday morning to discuss the decision.
The sum to be paid by Apple is 40 times bigger than any previous demand by the EC in such a case.
