Abaaoud, who Paris prosecutors on Thursday confirmed had been killed in a Wednesday morning gun battle with police, had his identity checked by federal police when he flew to Istanbul from Cologne-Bonn airport in January 2014.
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He said that he was planning to visit friends and relatives there and would return to Cologne by plane.
In fact, he never made that return trip.
"We can't make any sense [of his stay in Germany in 2007] at the moment," an investigator told Der Spiegel.
Abdeslam Salah, another suspect in the Paris attacks, travelled through Germany to reach Austria in September 2015, just two months before the Paris attacks, it emerged on Tuesday.