"I don't see them ever joining and I had never believed that it would happen," she said during a televised debate with Martin Schulz, her Social Democratic rival in elections later this month.
She added that she would speak with her EU counterparts to see if "we can end these membership talks".
Merkel's tough stance came after Turkey arrested two more German citizens this past week "for political reasons", infuriating Berlin.
The arrests brought the number of German political prisoners in Turkish custody to 12, at a time when ties between the two NATO allies were already at an all-time low.
The plunge in relations began after Berlin sharply criticised Ankara over the crackdown that followed last year's failed coup attempt.
The arrest of several German nationals, including the Turkish-German journalist Deniz Yucel, the Istanbul correspondent for the Die Welt newspaper, further frayed ties.
Yucel has now spent 200 days in custody ahead of a trial on terror charges.
After Steudtner's arrest, Germany vowed stinging measures impacting tourism and investment in Turkey and a full "overhaul" of their troubled relations.
Turkish President Recep Tayyip Erdogan, for his part, has also sparked outrage after charging that Germany is sheltering plotters of last year's coup, as well as Kurdish militants and terrorists, and demanded their extradition.
Erdogan added to the tensions this month when he urged ethnic Turks in Germany to vote against Merkel's conservatives and their coalition partners, the Social Democrats, in September 24 elections.
The escalating tensions have split the Turkish community in Europe's top economy, the largest diaspora abroad, which is a legacy of Germany's "guest worker" programme of the 1960s and 70s.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)