The Gunners were handed the tough test of facing the 2012 runners-up when the draw was made in Nyon on Thursday.
Germany striker Podolski will be especially keen to put one over his old club, where he spent an unhappy three years before joining Cologne in 2009.
"They are a big club - they played in the final in 2010 and last year - but we have a chance to win," insisted the 27-year-old.
"They have a very good team with big players. Mario Gomez up front, Franck Ribery, Bastian Schweinsteiger, Philip Lahm and Manuel Neuer.
"But there are two matches, home and away, and we have a chance to win."
Podolski is equally confident that Arsenal can overturn their inconsistent domestic form and mount a challenge for the Premier League title.
"Man United are in front, we have 15 points to first place and it's tough but the season is long. When we fight, play our game and don't lose stupid points we can go from fourth to first place."
While Arsenal face up to the traditionally busy festive fixture programme, with the FA Cup to follow, Bayern will shortly go into the winter break afforded to German teams.
However Podolski's fellow countryman Per Mertesacker feels Arsenal can turn schedule to their advantage.
"It's a long period for us while all the German teams will have a winter break and a rest," said Mertesacker.
"They only conceded seven league goals in the first half of the season but we will see what happens in February.
"We hope we can get into a good rhythm to face them and be a strong squad. Maybe it's a good opportunity for us to face them in February because we will be in our rhythm
"We have a lot of potential and Bayern know they will face an Arsenal squad which will be strong in February."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar