Bergkamp, who enjoyed a successful 11-year spell as a player with the Gunners and won three Premier League titles and four FA Cups, currently works as an assistant coach at Ajax.
He told The Telegraph: "The feeling Johan Cruyff has had for Barcelona, I have the same with Arsenal. At Arsenal it was a good click. I always enjoyed it. I never had a bad day there.
"It is always on my mind. It is part of my ambition to come back at some stage. I don't see myself being at Ajax for the rest of my coaching career. I don't see myself as a manager.
"I see myself as being part of the coaching staff. I really enjoy that role, especially the individual training with the strikers. Steve Bould is there now which is excellent. I've spoken to Patrick Vieira and Thierry Henry would love to come back to Arsenal one day. Tony Adams is a big option as well."
The 44-year-old recently released his autobiography that shared stories of his time at Highbury, including a few fall-outs with Wenger towards the end of his career.