The Gunners go to Anfield today.
Carragher wrote in the Daily Mail: "I've been a fan of his since I saw him at the World Cup finals in 2010 and I was genuinely excited about the prospect of the Germany midfielder displaying his skills in the Barclays Premier League.
"With four goals and eight assists, he has had a good start. But that is all it has been.
"Over the next fortnight, Arsene Wenger will want Ozil to show why he invested £42million in him; when you spend world-class prices on world-class talent, you want to see them produce in the games that matter."