The Germany international has divided opinion in the two years since his £42.5 million move from Real Madrid but Wenger is excited by his progress.
The Frenchman expects to see his charge scoring more goals in 2015-16 in addition to his usual creative passing and movement.
"He shows more authority to dictate the game than before," Wenger told the club's official website. "In the second part of last season, we saw the intelligence of his passing, the fact that he added some steel to his game, which was needed, and I'm confident that he can be one of the great players of 2015-16.
"You can see that people have turned in favour of him recently and he is starting to enjoy his game. He plays in the heart of the game and these kinds of players have an importance and can be efficient in helping us score goals.
"I also want more goals from him because he plays in a position [high up the pitch] and he's a good finisher. He doesn't take enough chances when he's in a position where he can finish. He's conscious of it and he wants to do it now.
"His main aspect will always be the intelligence of his passing and his creativity but he gets into positions where he can finish better and we want 10 goals per season from him."
While Wenger feels that Ozil has suffered from a lack of proper pre-season preparation in recent years, he believes that everything is starting to come together this summer as the German gets more settled in England.
The Gunners boss recalled: "He joined very late [in 2013] without any preparation with the team. In 2014 he came back exhausted after the World Cup, he got injured for four months and in the second part of the season he really started to adapt. This is the test and a very important season for him.
"He looks happy. London transforms people. At the start when people come from the south they feel a bit of a shock because of the climate, the city is bigger. After a while, London slowly gets people under the charm of the city and I've seen that many times.
"The Premier League is sometimes a shock for the players because they think: 'Oh, what's happening here?'. I remember when [Robert] Pires arrived and, in the first year, I put him next to me at Sunderland. I said: 'You will sit next to me today and watch the game'. After 20 minutes he said: 'Is it always like that?' and then he adapted."
