The 16-year old became Arsenal's youngest Premiership player when he debuted against Blackburn in September and Wenger is expecting for even bigger things.
"I believe he will end up a central midfielder, just off the striker in the Bergkamp role," Wenger said.
"I am convinced he will have a tremendous penetrative power and we forget that the boy is only 16 and already has so much power, you give him four more years and he will be massively strong.
"He can find the final ball and can also score goals. He is passionate and committed guy, he is not afraid of tackles and you want this type of player to finish off central.
"I would not like to put too much pressure on him because of the expectation level," he added.
"That is one of the problems you have when you are talented and very young, Theo Walcott went through that.
"At the start there is a lot of enthusiasm around players and suddenly afterwards people say 'oh he is not as good as we thought he would be' there is a lot of scepticism around the player.
"He has to survive at the top level and it is not easy. Theo coped well with that and I am confident we can surround Jack well enough to deal with it."