The German has been linked with an exit from the Emirates all summer, having fallen further down the pecking order since the arrival of Alexis Sanchez.
Galatasaray had been strongly linked with an interest in Podolski, but the Metro is now reporting that Wolfsburg have entered the race to sign the 29-year-old.
Podolski has previously refused to rule out a return to the Bundesliga, and a move is becoming more likely as competition for his spot has increased.
Arsene Wenger also admitted earlier in the summer that the club was likely to offload players before making any further recruitments, and Podolski could well make way for more squad additions.
Since arriving at the club in 2012 Podolski has struggled to nail down a starting role, and he expressed his dissatisfaction at being regularly substituted at the back end of last season.
The German was part of Arsenal’s FA Cup-winning side from last season, and has scored 28 goals in 69 appearances for the club.
Podolski would follow former Arsenal striker Nicklas Bendtner to the German club, having signed on a free transfer earlier this summer.