The 40-year-old was in Amsterdam on Tuesday, attending Ajax's final training session ahead of their Champions League clash with APOEL on Wednesday.
Campbell is pursuing his coaching qualifications and contacted Bergkamp, who is an assistant at Ajax, to set up the visit. The trip is one of several Campbell has scheduled to help gain his qualifications and he will be visiting a number of clubs.
Talking to Ajax's official website, Campbell said: "I hope to also catch up with Marc Overmars and Edwin van der Sar this week. It's interesting how many former players are back at Ajax in key positions. I'm very interested in the philosophy and training methods of Ajax."