The Gunners are said to be showing an interest in the Croatian international as they look to add a top-class striker to their ranks this summer.
Olivier Giroud led the line for the majority of last season and eventually ran out of steam as the North Londoners slipped from top spot to a fourth-place finish in the Premier League.
Giroud's understudy Yaya Sanogo is largely unproven at the top level, while unfancied Nicklas Bendtner has left on a free transfer to leave Arsenal seriously short of options up top.
Gunners legend Alan Smith backed the pursuit of the Bayern striker on Wednesday, but reports in Italy have now claimed that the Rossoneri are keen on Mandzukic.
Borussia Dortmund striker Robert Lewandowski will join the Bundesliga champions next season, and Mandzukic is said to be consdering his future at the Allianz Arena.
Die Roten's valuation of the forward is believed to be around £24 million, but the Italian giants, who finished a disappointing eighth last term, think that £19 million will be enough to snare the 28-year-old.
Mandzukic signed for Bayern from Wolfsburg in 2012 and has won the Champions League and two Bundesliga titles during his time at the club.