A "smart" Brexit deal could serve as a model for the EU's future relations with other non-EU states, German Foreign Minister Sigmar Gabriel says.
Turkey and Ukraine were two states that could benefit from the template, he told Germany's Funke media group.
He did not see either joining the EU any time soon, so alternative forms of closer co-operation were needed.
The UK's future relationship with the EU, which it is due to leave on 29 March 2019, is still being negotiated.
The two sides agreed this month on the three "divorce" issues that took up the first phase of negotiations: how much the UK owes the EU, what happens to the Northern Ireland border and what happens to UK citizens living elsewhere in the EU and EU citizens living in the UK.
In June 2016, the UK voted in a referendum to leave the EU after more than four decades of membership.
What did Sigmar Gabriel say?
"If we can reach a smart agreement with Great Britain that outlines its relations with Europe after Brexit, then that could serve as a model for other countries," he said.
He foresaw a "new, closer form of customs union" with Turkey, provided the situation in that country changed. That would appear to conflict with the UK's aim to leave the EU's customs union as well as its single market.
Germany is concerned at Turkey's human rights record under President Recep Tayyip Erdogan, particularly the recent arrest of several German-Turkish nationals.
"It's a good sign that several detained Germans have been released," Mr Gabriel said, but he added there was still great concern over imprisoned journalist Deniz Yucel. "The Turks know how important his fate is for us," he said.
What EU agreements exist with Turkey and Ukraine?
Under a specific customs union agreed in 1995, goods may travel between the two areas without customs restrictions although it excludes unprocessed agricultural products.
Talks on accession, however, have not moved since 2005.
An association agreement currently exists between Ukraine and the EU which fosters political co-operation and trade.
What will the 'Brexit model' be?
Nobody yet knows but the UK is due to leave both the EU's single market and customs union.
Agreement was reached on 8 December to move talks forward on to a proposed transition period after the UK leaves, and the future relationship.
But unlike the Canada deal, he also wants financial services included in the tariff-free area.
One headache for negotiators is the Irish border and how to maintain the flow of trade between Northern Ireland, which is part the UK, and the Irish Republic, which is in the EU.
Will Germany's position change?
Mr Gabriel, from Germany's social democrat SPD party, is foreign minister in the caretaker coalition government led by conservative Chancellor Angela Merkel.
After the inconclusive German general election in September, when Mr Gabriel's party fared badly, Mrs Merkel failed to form a new coalition without the SPD.
The SPD is now preparing for talks with Mrs Merkel on a new coalition.