The Gunners are without a trophy since 2005 but currently lead the Premier League and the record signing has warned their rivals that there will be no let up during the season
The midfielder smashed the Gunners transfer record when he completed a £42 million move from Real Madrid on transfer deadline day, and has pitched in with one goal and four assists to help the Gunners climb to top spot in the Premier League.
Arsenal's last piece of silverware came in the form of the 2005 FA Cup, but after winning 10 and drawing one of their past 11 games in all competitions, Ozil feels the only way is up for his new side.
"I am delighted we top the table," he told reporters. "But we also know that the season is still very long. To talk about winning the league would be too early. The current table is nothing more than a snapshot."
"We will continue to play every game with our full concentration, we will try to get better as a team. If we can do that, we have a great chance to achieve a lot. I will give it my all.
"For me the Premier League is the strongest league in the world. Every match is a challenge and the games are very intense.
"I believe, I can profit from that. The atmosphere in the stadium is also striking, the support of the fans, also of the away fans, is impressive."
Ozil's former manager at Real Madrid, Jose Mourinho, previously called the midfielder the "best No.10 in the world", and while the German appreciates such remarks he says it has no affect on his performances.
"Such compliments flatter me," he told reporters. "I'm grateful for that.
"I do not need them though since I do not draw confidence from the statements of others. I know what I can do. And everyone who works or worked with me know too."
Ozil also thanked the German contingent of Per Mertesacker, Lukas Podolski, and Serge Gnabry at the Emirates Stadium, with their presence having aided his adaption to life in England.
"The guys are all great, they help me and support me really well," he continued. "For many reasons, this is a huge help for me. I have to admit that my English falls short, I definitely have to work on it.
"It's hard to 100 per cent judge the strength and abilities of the team-mates and the opposing players. [The squad] are looking for me on the pitch, they trust me, feed me with balls and respond to my ideas."