Der Spiegel magazine said that foreign intelligence services had picked up the content of communications by some "known international jihadists", without giving specific details.
The intelligence, which was passed to German authorities, indicated they had discussed possible attacks on the rallies organised by the so-called group, "Patriotic Europeans Against the Islamisation of the Occident" (PEGIDA), the magazine said in a pre-released story to appear in this weekend's edition.
"We take these leads very seriously," Spiegel quoted an unnamed high-ranking security official as saying.
PEGIDA marches began in the eastern city of Dresden with several hundred supporters three months ago and have steadily grown, to number 25,000 on Monday, five days after the attacks in Paris by Islamists, in which 17 people were killed.
Several other cities have seen smaller copycat rallies.
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