Wenger stunned the footballing world on Friday when he announced he will leave the Premier League club at the end of the season after nearly 22 years in charge.
Podolski - who spent two-and-a-half years working under the Frenchman at the Emirates Stadium - is intrigued to see what direction his former employers go in as they begin their search for a new manager.
The World Cup winner believes Carlo Ancelotti is an ideal candidate if Arsenal, who appointed German Sven Mislintat as head of recruitment last November, want someone with experience - but could see them instead looking for a younger option to take charge.
“If someone was in a club for 22 years, he leaves a lot of marks,” Podolski said in an interview with Die Welt .
“I’m curious which successor they decide on. It’s a question of whether they want someone with experience like Arsene Wenger, a guy like Carlo Ancelotti, or maybe a young, hungry coach.
“I think Arsenal would be good for a German coach. That is my feeling. The club has been relying on German know-how for several years now.”
Podolski has fond memories of his time under Wenger, including winning the FA Cup at Wembley in 2014.
“I got along great with him. He’s a cool, laid back guy,” he added.
“He never gets loud, is always calm - a gentleman. He is a great coach. And he was also always having fun.
“I always had the feeling that I had with Joachim Low or Jupp Heynckes.
“They are coaches who clearly knew what they wanted but did not annoy their team - and they [the team] usually paid them back.”
