The German Chancellor wants a EU-UK relationship "as close as possible" once Britain has left the bloc in 2019.
May has previously drawn criticism for appearing to link security - in which Britain is a major player -with her hopes for a new trade deal with the EU.
Brussels and London have to start next month negotiations on the conditions of the transition period that the European Union expects to continue until December 31, 2020.
The German chancellor said she believed that it could be possible to agree a bespoke deal rather than a traditional model, such as those with Norway and Canada.
Mrs May, who will speak in Munich on Saturday about her plans for a close security relationship with the European Union after Brexit, said the Government would set out more about its plans for the economic partnership "in the coming weeks".
Earlier on Friday, British government officials said London was gearing up to push for the kind of Brexit plan on financial services that the City of London has long favoured, but which has already run into opposition in Brussels.
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Mrs Merkel said: "We basically have not changed our stance on Britain leaving the European Union".
"I will reiterate that the United Kingdom remains unconditionally committed to European security and set up my vision for a unique partnership between the EU and the United Kingdom on defence, information sharing, security and law enforcement", she said.
"We have, at different stages, set out and clarified different aspects of the future relationship that we want to have with the European Union".
Mrs May also insisted there would be no return to a "hard border" in Northern Ireland and said there were various ways the issue could be addressed.
As part of her trip to Germany, the Prime Minister will outline her wishes for a future security EU-UK partnership in a speech at a security conference in Munich on Saturday.
But she will warn: "This can not be a time when any of us allow competition between partners, rigid institutional restrictions or deep-seated ideology to inhibit our cooperation and jeopardise the security of our citizens".
The end of limbo in Germany?
"Because as the threats evolve, as they grow, as they don't recognise borders, so we need to continue that cooperation and be able to adapt to the threats as they come".