Sigmar Gabriel said a “smart” deal by Brussels would serve as model for ties with other nations.
He said the likes of Turkey and Ukraine did not want to join the EU but were seeking a closer relationship to it.
Mr Gabriel told the Funke newspaper group: “I can’t imagine Turkey or Ukraine becoming EU members in the next few years.
“If we get a smart agreement with Britain regulating relations with Europe after Brexit, that could be a model for other countries – Ukraine and also Turkey.”
The comments give a boost to Theresa May as she looks to move negotiations on to future trade with Europe.
EU chiefs are not keen on a bespoke Brexit deal, seeing it as encouragement for other member states to leave the bloc.
Chief negotiator Michel Barnier has previously said a bespoke deal for Britain is off the table.
Earlier this month, he stressed any deal will not replicate the kind of access London financial services firms have now.
And he has repeatedly said while a trade pact will be tailored to the specifics of the British economy, it will follow the broad outlines of the Canada treaty, without bespoke advantages.
Brexit Secretary David Davis has called for a “Canada Plus Plus Plus” deal, implying better access than the Canadians in some areas.
And Mrs May has said she will use Britain’s size and importance to its European neighbours to negotiate the most favourable future relationship.
Before the Christmas break, Mrs May told MPs an unnamed EU negotiator had assured her Britain would get bespoke trading agreements.
She said: “One of the senior members of the negotiating team has made very clear that the United Kingdom can indeed have its own, if you like, bespoke agreement in terms of trade for the future.”
Turkey, a candidate for EU membership for decades, already has a customs union with the EU which allows the trade of most goods without tariffs.
One possibility would be to offer Ankara a “new, closer form of the customs union”, Mr Gabriel said, although such a project would have to wait for changes in Turkey’s political environment.
An agreement between the EU and Ukraine on a “deep and comprehensive free trade area” formally came into force in September, aimed at allowing free trade of goods, services and capital, and visa-free travel for people for short stays.