The Gunners have not been crowned the best team in England since the 'Invincibles' season of 2003-04, while their last silverware came in the form of the 2005 FA Cup final triumph over Manchester United.
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|25/1||Arsenal are 25/1 with Bet365 to win the Champions League
"It will not be easy," he told The Daily Mirror. "Everyone thinks it's easy to get a trophy.
"You have five or six teams who fight for first place. It's not like in Spain where it's just two teams and in Germany you just have Dortmund and Bayern.
"It's not easy in England. It's so competitive.
"At Arsenal we have good players, a great coach and great fans. If we can pull it together then I believe we can win the Premier League."
Podolski finished third in the club's goalscoring charts last season behind Theo Walcott and Olivier Giroud, and is hoping to raise his performances for the new campaign.
"I will try to play better, score more goals and do some assists for Arsenal," he added. "It's very important that we qualify for the Champions League and fight for the championship.
"It was my first year and I'm very happy. We will see how much I can improve and whether I can get better."