Podolski will link up with the Gunners later in the summer after a deal was agreed in April for the striker to move to the Emirates Stadium from Cologne.
The Germany international is currently in action at Euro 2012 and will win his 100th cap on Sunday if selected against Denmark.
He would like to think that Arsenal's fans are excited about what they are seeing and hopes to impress in the Premier League next season.
"I don't think I have anything to prove to Arsene Wenger. He has seen me play several times and knows what I can do," said Podolski.
"I think it is clear that my transfer was no accident and, of course, I'm very glad I signed with Arsenal.
"In fact, what has really pleased me is that Arsenal fans can watch me play in a tournament like this and realise what I'm capable of at the highest level.
"Very soon I will also show that in London."