BVB failed to beat the Gunners in their 2011-12 group stage matches with Arsene Wenger's side winning 2-1 at The Emirates and holding Klopp's team to a 1-1 at Westfalenstadion.
However, the German has revealed that he is plotting revenge against Wenger's men after being drawn alongside the Gunners, Marseille and Napoli in Group F.
"The fact is, we have a score to settle with Arsenal and with Marseille," Klopp was quoted as saying on the club's official Facebook page.
"It's a great, evenly-balanced group with four teams that all have what it takes to progress from the group stage.
"I've never been to Napoli but I'm really looking forward to the atmosphere. It's going to be very exciting."
Dortmund were runners-up in last season's competition, eventually going down to domestic rivals Bayern Munich.