Bergkamp, who is coaching at Ajax, suggested he would like to return to Arsenal in the future. But the fact he refuses to fly would rule out any European trips.
How could a team cope without a manager for European travels.
Arsene Wenger: "I am not against it one day. He has the qualities, but you need to have the need as well because we have a big staff already.
"He is now at two clubs that made Dennis Bergkamp. The first, and certainly the most important one, is Ajax.
"He is at Ajax now and a coach there. The second club that is important in his life is Arsenal. Maybe that will be the next step."
Wenger left out club-record signing Mesut Ozil, who had missed an early penalty against Bayern, because of a thigh problem.
Arsene Wenger: "It was a kick. He should also be available next week. He is in the dressing room at the moment."