The leading German newspaper Sueddeutsche Zeitung cites diplomats in Brussels as saying Berlin won't sign the deal in its current form.
The newspaper report says the sticking point for the German government is over legal protections granted to investors.
A spokeswoman for International Minister Ed Fast will only say negotiations to finalize the agreement continue.
Canada and the EU reached an agreement in principle on the deal last October after four years of negotiations.
The Harper government trumpets the deal, known as the Comprehensive Economic and Trade Agreement, as one of the biggest ever -- one it says could benefit Canadian business more than NAFTA.
The setback could be politically damaging to Prime Minister Stephen Harper, who has staked his government's reputation on the potentially lucrative agreement.
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