Britain voted to leave the European Union in June 2016, becoming the first country to seek a divorce from the bloc, which includes Germany but not Turkey.
"If we are able to get a smart agreement with Britain that governs its relations with Europe after Brexit, it could be a model for other countries: Ukraine and Turkey," Sigmar Gabriel said in an interview with German media group Funke, published on Tuesday.
"I can't imagine Turkey or Ukraine becoming EU members in the next few years," he said. "This is why we have to consider other ways of close cooperation."
Earlier in December, Britain and the EU agreed on Brexit terms to establish a future relationship.
The deal includes details of a financial settlement, the Irish border and rights for citizens hit by Brexit.
Turkey has been in full membership talks with the EU since 2005, but these discussions have essentially been frozen over the past few years. Ukraine is not yet a candidate country for membership.
In response to Gabriel's comments, Markar Esayan, an MP with Turkey's ruling Justice and Development Party (AK Party), told Al Jazeera that the nature and conditions of Ankara's full membership talks were clear and irrelevant to the Brexit process.
"This statement shows that the conditions for Turkey in membership talks are different compared to the other candidate countries, as none of them are offered a separate path," said Esayan, who has a role on the country's committee on EU harmonisation.
"The EU cannot make Turkey responsible for not letting the country into the bloc. If it does not want Turkey as a member, it should officially take decisions in this direction at EU institutions, rather than politicians making such arbitrary statements."
Relations between Ankara and Berlin have been tense since last year's failed coup in Turkey, in part over the imprisonment of German journalists and activists by Turkish authorities on "terror" charges.
Germany and other EU member states have condemned the Turkish government's detentions and purges of tens of thousands of people after the July 2016 incident.
Deniz Yucel, a prominent German journalist and critic of the Turkish government, is among the German citizens who remain imprisoned while Mesale Tolu, another German journalist, and Peter Steudtner, a German human rights activist, have been released pending trial.
Local and international rights groups accuse the government of using the coup attempt as a pretext to silence opposition in the country.
Ankara says that the purges and detentions are aimed at removing supporters of Fethullah Gulen from state institutions and other parts of society.
Gulen is a US-based, self-exiled religious leader who Ankara blames for the attempted coup. He denies the charge.
EU cuts Turkey's funds
The EU recently shrunk so-called "pre-accession funds" for Turkey for the first time in the 2018 budget, due to what it called the country's "deteriorating situation in relation to democracy, rule of law and human rights".
In March, before a referendum to change Turkey's parliamentary system to an executive presidency, the Netherlands, Austria, Germany and Denmark prevented Turkish politicians - including ministers - from taking part in rallies within their borders to back a "Yes" vote.
This led to an unprecedented diplomatic crisis.
Bulgaria, which will take over the EU presidency on January 1 for six months, said in its programme that the bloc's enlargement policy would be "a key priority" for its term, with focus on the Western Balkans, with Turkey not included in this prospect.
"A specific priority of the Bulgarian Presidency is the European perspective and connectivity of the Western Balkans," the Bulgarian government said in a programme adopted by its Council of Ministers earlier in December.
"EU Enlargement Policy … continues to be the most effective instrument for guaranteeing peace, stability and prosperity in the Western Balkans," it added, while merely referring to "continuing dialogue and cooperation" with Turkey.
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