The 30-year-old Germany international??is currently on holiday in Turkey and is understood to be speaking to the Super Lig Champions.
Podolski, who has a year left on his Arsenal contract, spent the second half of last season on loan at Serie A club Inter Milan.
Podolski’s six-month spell in Italy only fashioned one goal in 18 appearances in all competitions, having found his first-team opportunities limited under Arsene Wenger.
He failed to make a Premier League start in the first half of last season, but scored three goals in six cup appaearances.
Podolski, who has 125 caps and 48 goals for Germany, signed for Arsenal from FC Koln for ??11m in 2012, and since made over 80 appearances for the Gunners, scoring 31 goals in all competitions.
He began his career as a FC Koln trainee before a three-year spell at Bayern Munich.