The midfielder, 28, was linked with a move to the Gunners last year before he joined the Bundesliga giants from RB Leipzig.
Mikel Arteta is looking to bolster his midfield this summer after struggling to cover the absences of Thomas Partey last season.
According to Bild, Sabitzer has been put up for transfer by Bayern just 12 months after joining the German side.
The report goes on to say that the player could be available for £13million – the figure his current club paid for his services last year.
Sabitzer made 30 appearances for Bayern last season but scored just one goal as he struggled to settle at the Allianz Arena
The Austrian could be a good option for Arteta with the Spaniard having already revealed that he will need to manage his resources in the transfer market.
Arsenal have qualified for the Europa League next season and need a bigger squad to cope with the extra matches.
But the north Londoners face forking out considerable fees to secure targets such as Leicester’s Youri Tielemans and Manchester City’s Gabriel Jesus.
Speaking earlier this year, Arteta explained that he wants 22 top quality outfield players and three goalkeepers for next season.
He said: ‘Both competitions (the Champions League and Europa League) require a much larger squad because the number of games you play is much bigger, so I don’t think it makes a lot of difference (which competition Arsenal qualify for).
‘If you can afford it, and we don’t have to do the turnaround in the squad that we’ve had to do, if you ask me what I want it’s 22 outfield players and three goalkeepers.’
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