The German international is understood to be among a handful of players who could leave the Emirates Stadium ahead of next season.
However, the 28-year-old is eager to remain with the Gunners following an "outstanding" two years in North London.
"Going to London was the right step," he is quoted as saying by Goal.com. "I had the chance to go to a big club and to play in the strongest league in the world. I am happy in the city, in the league, in the club. Those two years have been outstanding for me."
Podolski scored 12 goals in 27 games for Arsenal during the 2013-14 campaign.