The European Commission will withdraw its complaint against Ireland for not recovering 13 billion euros ($16 billion) in unpaid taxes from Apple, but only if the country recovers that amount in full, the EU's Competition Commissioner Margrethe Vestager told CNBC.

The EU took Ireland to the European Court of Justice last October for failure to recover the sum from the technology giant, when it was ruled that Apple had benefited from illegal tax benefits in Ireland in August 2016. According to EU law, the recovery of funds should usually take four months after the Commission issued its decision.

"In our opinion, it (recovery of unpaid taxes) has taken too long. But from what I hear from the Irish, they are getting there. So, of course, we hope that soon, the recovery can happen in full, because if that happens we will withdraw the complaint that we have filed with the courts," Vestager told CNBC in an interview Monday.

Media reports last week suggested that Ireland is calculating how much money Apple needs to pay back and that such calculations should be done before the end of April. So far, the Irish authorities said that their estimations are close to the commission's 13 billion euro figure.

Speaking to CNBC, Vestager said it has taken Ireland "too long" to recover the money, but she understands that the process is complex.

"Of course, we look at the difficulties that (are) related to the case," she said. "But it is important for us that it happens, and this is why… On the process alone of recovery, unpaid taxes, we have asked the court to look into it."