The 27-year-old has been identified as a possible replacement for Bacary Sagna, should the France international leave north London at the end of the season.
Gunners boss Arsene Wenger is believed to be running the rule over a number of different right-back options, as Sagna's contract dispute continues, with a view to adding competition for Carl Jenkinson at the Emirates Stadium.
Piszczek is regarded as Arsenal's first-choice target following another impressive season in Germany, having also helped the Bundesliga giants to this year's Champions League final at Wembley.
The Poland international has been watched extensively by Premier League scouts since he rose to prominence at Euro 2012, when Chelsea weighed up a bid to bring him to Stamford Bridge after Jose Bosingwa was released on a free transfer.
However, former Blues boss Roberto di Matteo opted instead to sign highly-rated Spaniard Cesar Azpilicueta, who has impressed in his debut campaign in west London.
Arsenal could now bid unchallenged, for a player that signed for Borussia Dortmund in 2010 on a Bosman free transfer from Hertha Berlin.
Piszczek has gone on to establish himself as one of the best full-backs in the Bundesliga, and would be a welcome addition to any Premier League club this summer.