Arsene Wenger's latest team are setting the early pace this season and, after seven games, are top of the Premier League table on goal difference.
He also said he would like to return to the club sometime in the future but 'did not see myself as manager'.
Giving a rare interview in the wake of his recently published autobiography, the 44-year-old Dutchman admits he is a keen student of the game and is now back at Ajax as a coach, the club where he learned the ropes as a teenager.
As for Arsenal's excellent start to the season, Bergkamp told Sky Sports News: "I see a lot of freshness in the team.
"They are similar to my time at Arsenal. They have good movement, commitment, and a good passing game.
"They know what they want to do and what they need to do to go forward.
"It's enjoyable to watch but it's effective as well - which is good after something was missing these past few years."
Bergkamp collected three Premier League medals during his time at the club - all at Highbury - along with four in the FA Cup.
As for his career as a coach and his future, he added: "I'm settled here (Ajax).
"We've started something here and I'm looking forward to staying here for a few more years.
"I would love to go to England some time, preferably Arsenal. But I don't see myself as a head coach or manager. I see myself as part of a coaching team."
He also admitted that Spurs legend Glenn Hoddle was one of his inspirations when growing up in the Netherlands: "He had great control with both feet and was a superb passer."