Ginter has been consistently linked with the Gunners after a strong first full season in the Bundesliga, helping Freiburg finish fifth with a series of accomplished displays in a defensive midfield role.
The German side have insisted that reports of a £6.1m bid from Arsenal are wide of the mark and are determined to keep the 19-year-old for at least another season.
Freiburg's sporting director Joachim Saier told reporters: "There have been no offers for Matthias, and to suggest we have agreed a fee, as mentioned, is nonsense. The fact of the matter is, we have no thoughts about selling him."
Ginter's performances earned him a call-up to Germany's squad for the European Under-21 Championships earlier this summer, where he played three matches in central defence.