Ursula von der Leyen hopes to be confirmed as president of the European Commission. "I still hope you will remain", she told a hearing in the European Parliament ahead of a vote on her nomination next week.
Von Der Leyen will take over from Jean-Claude Juncker in November.
As part of her pitch on Tuesday, Mrs von der Leyen tackled the thorny issue, calling on British lawmakers to take responsibility for sorting out the UK's departure.
"Though I still hope you remain, it is in our interests to have you sort things out".
The conservative German defense minister may still win support of the full parliament next week, but rejection by the Greens leaves her relying more on nationalists in eastern Europe who like her tough stance on Russian Federation.
In a subsequent hearing on Wednesday, this time with the Greens group, UK MEP Molly Scott Cato said that although not all of von der Leyen's answers had been received "very warmly" during the hearing, she was "delighted to hear" von der Leyen express the hope that Brexit never happens, adding, "because I agree with you about that".
The latter comment was made in reference to the controversial Irish backstop, which to date the Europeans say they will not renegotiate, but which the United Kingdom fears could either lock it in regulatory alignment with the EU permanently - preventing the United Kingdom making future independent trade deals - or threaten the union if Northern Ireland remains in the Customs Union whilst Great Britain diverges after the implementation period.
The EU, weakened by the 2009-2012 euro zone crisis, Britain's decision to quit the bloc and the rise of far-right and far-left eurosceptic parties, needs a strong Commission president to improve its fortunes, officials and experts say.
Von der Leyen, who would be the first woman to lead the EU executive, said she wanted an equal share of men and women as European commissioners. "We have an agreement - which hasn't been signed on both sides - and we have the backstop", she said, referring to a controversial provision in the deal negotiated by Mrs May to avoid extensive border controls on the Irish border after Brexit.
Speaking in a mix of English, French and German, Von der Leyen emphasised her European outlook, reminding MEPs she was born in Brussels and attended the city's European school with Dutch, German and French classmates.
She clarified her views on European defence, restating that national parliaments should continue to have the final say on sending men and women into unsafe situations.
Although it is expected Von der Leyen will be approved by the European parliament, she still faced sniping over the process of her appointment whereby she leapfrogged politicians who had declared bids to lead the commission before European elections.
"What she will do concretely is unclear", he added.
In her opening remarks Von der Leyen said the rule of law was "the jewel in the crown of our work" and that the European Union needed a mechanism for upholding it in member states.