The 19-year-old defender-cum-midfielder had been linked with a €7 million move to the north London club, with Arsene Wenger looking to bolster a backline that is without the injured Thomas Vermaelen.
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"That's nonsense. We have not received an inquiry and there are no thoughts about selling him," Saier told Badische Zeitung.
Freiburg's insistence that Ginter is not for sale is another blow to Arsenal during a disapointing summer window, having already had a £42m bid for Luis Suarez rejected and with Yaya Sanogo the only new arrival.
Ginter has made 23 Bundesliga appearances last season for Freiburg, playing predominantly at centre-back, and scored his only goal of the season in February against Werder Bremen.