The German admitted that Champions League qualification is the most important goal this season but refused to rule out the possibility of the Gunners being crowned champions in May.
Podolski told the Daily Mail: "First of all, to be in the top four with Arsenal so that we qualify directly for the Champions League. That is our most important goal.
"The other goal is of course to fight for the Premier League title. You won't have any idea of the front runners until after 15, 20 games, and obviously if you play for Arsenal, in the Premier League, there is only one goal, to be among the front-runners for the title and that is what we are fighting for."
Podolski has netted four goals in 12 appearances this season.