The German striker joined Arsene Wenger's side this summer from Koln in a 10 million pounds deal after spending three seasons in his second spell at his hometown club.
Podolski feels it would be great to play alongside the Dutchman, but admitted he has no say in the matter of whether the skipper decides to leave the club.
"All I can say is Van Persie had an amazing record last season and hopefully there is a way he can stay with Arsenal. It would be great to play with him, but obviously this is not in my control," Podolski told ESPN.
The 27-year-old believes criticism that has come the way of Wenger is incredibly harsh considering his record with the Gunners, and feels the Frenchman is under-appreciated.
Podolski explained: "He has a record getting Arsenal into the Champions League every season and his reputation in Germany and all over Europe is very strong. What I like about him is his passion for attacking football. He aims to play with style and flair all the time.
"Those are his principles and he'll never compromise on them. Some people are disappointed with him, but they need to realise what a great coach they have.
"Mr Wenger could have moved on to another club, I am sure, but instead chose to stay and build something over the long term. He lives and dies by his own ideas and Arsenal is his baby.
"His reputation has been built on improving players and if he can help me take my game up a notch or two I'll be delighted. Back home in Germany, football people think very highly of Arsene Wenger. They listen to what he has to say and admire his achievements."
The striker is determined to end the Gunners' seven-year trophy drought but Podolski also feels the players need to perform better in the Premier League than they have in previous seasons as he thinks Champions League qualification is the least they should aim form.
He continued: "We have to try and achieve both. Arsenal have a quality squad and they should not aim to finish behind the rest or just settle for top four. Champions League football is the minimum requirement at Arsenal, but we should aim higher.
"For me, we have as good a chance as anyone in the Premier League. The key will be to start well and, unlike Manchester City or United, there will not be as much pressure on us."
The German international admitted it was a difficult decision to leave Koln but felt it was the right time in his career to do so although he has not ruled out a return to his former club in the future.
"Koln are the club of my heart. How could it be any other way when I've spent 14 years of my life there. They will always be special to me and it was a real wrench to tear myself away," Podolski said.
"Hopefully one day I'll return, but I just felt that, at the age of 27, I'd come to a crossroads in my career. The time was right for something new.
"With all respect to Koln, they couldn't offer me the Champions League and I wanted to test myself again at a top European club. Arsenal fit the bill in every way."