Oettinger, the European Commissioner for the budget and human resources, also said it was likely Germany would face "manageable" additional payments in the single-digit billion-euro range as a result of the Brexit budget "black hole."
The German official's comments came on Sunday in an interview with Germany's Bild newspaper.
Also at the weekend, it was claimed UK negotiators are now prepared to pay up to €37bn to the EU to settle the Brexit divorce bill. A senior UK government source, however, later said that "no such figure has been agreed".
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Elsewhere, Simon Fraser, a senior official at the UK Foreign Office until 2015, has said that the UK's Brexit negotiations have not begun well amid "differences" inside the cabinet.
Fraser, former head of the diplomatic service, said the UK side had been "a bit absent" from formal negotiations in Brussels.
He said he feared divisions within the cabinet were preventing the government from presenting a united front.
"The negotiations have only just begun, I don't think they have begun particularly promisingly, frankly, on the British side," he said.
The UK government is expected to publish position papers on key issues soon and a spokesperson for the Department for Exiting the EU refuted the claims, saying negotiators had already made "good progress on a number of issues".
The spokesperson said, "It is important that both sides demonstrate a dynamic and flexible approach to these negotiations.
"Government officials are working at pace and we are confident we will have made sufficient progress by October to advance the talks to the next phase."
The rebuttal comes with David Davis, the UK's Brexit secretary, currently on an EU wide charm offensive.
He has been to Germany, Denmark, Sweden, Finland, Slovakia, all three Baltic states, Spain, Portugal, Hungary, Poland and the Netherlands to make his case for a good deal.
Meanwhile, the Irish Prime Minister has proposed an EU-UK custom union and a transition period for the UK as a way of keeping an economic open border between Ireland and Northern Ireland after Brexit.
"If the United Kingdom does not want to stay in the [EU] customs union, perhaps there can be an EU-UK customs union," Leo Varadkar said during his first visit to Northern Ireland on Friday (4 August).
"We have one with Turkey. Surely we can have one with the United Kingdom?" he noted in a speech at Queen's University Belfast.
He said that he also favoured the UK joining the European Free Trade Association (EFTA) - alongside Iceland, Liechtenstein, Norway and Switzerland - as a way for the country to remain associated with the EU single market.