After more than an hour of talks between Mrs May and DUP leader Arlene Foster on Tuesday, Mrs May said the discussion had been productive.
It had been suggested the start of negotiations could be delayed by the failure of any party to win a House of Commons majority at last week's General Election.
Talks between the Conservative party and the DUP ended today without a conclusion.
Mrs Foster said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".
The first round of formal negotiations on Britain's withdrawal from the European Union will begin on June 19, it has been confirmed.
In a hint at a softer approach, Mr Davis said on Monday "we will start down this process" by focusing on the divorce proceedings from the European Union before moving on to trade.
May had called the vote early in hopes of strengthening her majority going into talks on exiting the European Union, but instead found herself in negotiations with a small party in Northern Ireland in order to stay in power.
Downing Street has warned that direct rule from London could be imposed if no solution is found before the June 29 deadline.
The negotiations with the DUP revolve around support from the party on a vote-by-vote basis in parliament, rather than a formal coalition government.
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But a deal with the DUP also risks destabilising Northern Ireland by increasing the influence of pro- British unionists, who have struggled for years with nationalists.
A source said: "The focus will be on restoring devolved government to Northern Ireland as soon as possible".
The proposed deal would see the DUP back the Conservatives in votes on the Budget and on any confidence motion while other matters would be negotiated on an issue-by-issue basis.
"Delay to deal with DUP means likely postponement of Queens speech; and possibly Brexit talks", BBC political reporter Norman Smith said on Twitter.
The talks later continued at Westminster without Theresa May after she left for Paris for a pre-arranged meeting with newly-elected French president Emmanuel Macron.
Asked about Schaeuble's comments, Macron said the EU's door was still open for Britain as long as the negotiations were not finished, but that it would be hard to reverse course.
Theresa May desperately needs the Democratic Unionist Party's 10 seats to pass legislation.
But now a number of senior Conservative figures say a Brexit deal, which leaves the United Kingdom inside the Single Market or the Customs Union is preferable.
Former Prime Minister David Cameron said May needed to listen to rival political parties, and that there would be pressure for a softer Brexit that would give greater priority to a close trading deal with the EU.
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