Van Persie, 22, is already being tipped as the long-term replacement for his compatriot and Arsenal's veteran forward but Henry believes the he should try to make his own name in the game rather than emulate Bergkamp's style.
Van Persie is enjoying a superb run of form for the Gunners after inspiring them to a draw with Tottenham at White Hart Lane, scoring a late double against Sparta Prague in the Champions' League and hitting a stunning opening goal in their home win over Sunderland.
But, despite Van Persie's rise to prominence, Henry says he cannot be compared with Bergkamp. Henry said: "I don't think there can be another Dennis Bergkamp. Dennis is Dennis. Robin can have his own way. Robin likes to dribble whereas Dennis will kill with a pass. It is difficult to compare."
However, Henry is full of admiration for the way Van Persie has applied himself at Highbury this season. "Robin is really confident," Henry said. "He has everything a footballer would dream to have. Robin can play anywhere he wants. It is up to him and his desire. One thing I like about him is that he wants to go and score.
"That is the most important thing. The first goal at home to Sunderland was amazing. Sol put in an incredible ball and Robin made a run behind their defence. He has done that a lot - he just wants to put the ball in the net. When someone has that attitude there is no stopping them."
Henry enjoyed an fine partnership with Bergkamp and the suggestions are that he could repeat the success with Van Persie. "He loves to play football, so do I," Henry said. "He likes to try stuff, so do I. When two people are of the same vision you can produce good football."Reuse content