The Bavarians edged past the Gunners in the knockout stages last campaign and the Allianz Arena boss is worried about the threat the English side could pose
The Bavarians drew 3-3 on aggregate with the Gunners last season at the same stage en route to winning the European title, edging through on away goals, but Arsene Wenger's side have looked a better outfit in 2013-14.
Pep Guardiola will be hoping he can imitate Jupp Heynckes' navigation of the round of 16 at the north London club's expense, but Rummenigge is under no illusions as to the quality of Arsenal.
"There were more convenient and easier opponents in that pot," the former West Germany star told reporters after Monday's draw in Nyon. "I'd rather have played Zenit than Arsenal.
"But we are not wishing against the draw either. We know we will meet an opponent that deserves lots of respect. We have to perform well twice.
"With their three Germans [Per Mertesacker, Mesut Ozil and Lukas Podolski] in tow, they are seeing more stability and are experiencing a good season."
Bayern are currently preparing to play in the Club World Cup, with a semi-final against Guangzhou Evergrande on Tuesday.