The Dutchman is currently assistant coach at Ajax.
"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," Bergkamp told the Daily Telegraph.
"I've spoken to or have heard about others [former Arsenal colleagues] who would also love to come back.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball