The Germany international is wanted by the eastern European outfit this summer, Milliyet reports.
The Germany international has become something of a forgotten man at the Emirates Stadium, with the likes of Alexis Sanchez and Danny Welbeck overtaking him in the pecking order since arriving in North London ahead of this season.
As such Podolski did not start any Premier League games in the first half of the 2014-15 campaign and has been subsequently loaned out to Italian side Inter Milan.
With the former Bayern Munich forward not showcasing his best form in Italy and yet to score a goal for Roberto Mancini’s men, a return to the Arsenal first-team fold appears unlikely next term.
Galatasaray are reportedly keen to give Podolski the first-team action he craves and will look to make him one of their designated foreign players this summer.
The story also suggests that the Turkish outfit made an unsuccessful move for Podolski in January but are not deterred and will revisit their interest at the end of the current campaign.