The German club have been drawn alongside the Gunners in Group F of the 2013/14 UEFA Champions League group stage and Klopp is looking to exact revenge on Arsene Wenger's men after they drew 1-1 and lost 2-1 during the 2011/12 European campaign.
"It's a great, evenly-balanced group with four teams that all have what it takes to progress from the group stage," Klopp told the club's official Facebook page after being drawn with Arsenal, Marseille and Napoli.
"The fact is, we have a score to settle with Arsenal and with Marseille.
"I've never been to Napoli but I'm really looking forward to the atmosphere. It's going to be very exciting."