The 29-year-old joined the Gunners from FC Koln in 2012 and helped the club to lift the FA Cup in May.
However, he has occasionally found himself left on the bench and he appeared just 20 times in the Premier League last season.
According to Sky Sport Italia, Juventus have made an enquiry for the German international, who is said to be high on their list of targets.
It is believed that Bianconeri manager Massimiliano Allegri is an admirer of Podolski due to the variety of positions that he can operate in.
Podolski has scored 28 goals in 69 appearances for Arsenal.