The 21-year-old has just one year remaining on his current contract at the Emirates and he is yet to pen an extension.
Arsenal are keen for the German to agree fresh terms and they are ready to sit down for talks with him, with Arsene Wenger recently in a recent interview that he is expected the youngster to stay at the club for a long time.
However, according to Sky Germany, Bayern Munich have muscled in and are trying to lure Gnabry to the Allianz Arena.
The Bundesliga champions have been impressed by the youngster’s performances at this summer’s Olympics, where he finished as joint top-scorer and was named Germany’s Player of the Tournament.
They are now prepared to test Arsenal’s resolve by making a formal offer for Gnabry, with Bayern aware about the short amount of time left on the player’s contract.