Lukas Podolski's agent has told Bild there is "concrete interest" in the Arsenal forward.
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The newspaper reports that Galatasaray are the favourites for the 29-year-old Germany international.
Podolski is under contract at the Emirates until 2016, but faces competition for regular playing time following the arrival of Barcelona attacker Alexis Sanchez, 25, and the return of Costa Rica international Joel Campbell.
According to the Mirror, Arsenal boss Wenger has already given the go-ahead for Podolski to leave the Premier League side.
"There have always been enquiries," Podolski agent Nassim Touihri told Bild. "But now there is also concrete interest from other clubs. But Lukas feels great in London."
The 116-time Germany international has a variety of clubs and leagues to choose from, Bild reports.
According to the paper, the Turkish side Galatasaray, who have been after the attacker for a number of years, lead the race as the former Italy coach Cesare Prandelli is looking for major reinforcements ahead of their Champions League campaign.
Bild also mentions interest from MLS as well as Spain and Germany, where his former club Cologne have already ruled out a return of the forward.