The Gunners finished fourth in the top flight last campaign, securing Champions League football for 2013-14, despite losing striker Robin van Persie to Manchester United.
Podolski told The Sun: "The hope is that this season Arsenal will be at the top of the league. English football, thankfully, is not like Spain where you only have two teams — Barcelona and Real Madrid — who fight at the top.
"In the Premier League you have five, six, even seven top, top teams. It is very difficult but I know that Arsenal are one of those top teams who will be involved.
"You don't know how the season will work out. A few of the other teams all have new managers so it is difficult to say. But they will be strong and equally, Arsenal will be strong."
Podolski scored 16 goals in his debut season in the Premier League for the Gunners.