Arsenal have not made it beyond the round of 16 since 2009-10, when they lost to Barcelona in the quarter-finals.
Ozil believes the Gunners have been “unlucky” in that time, though, due to frequently drawing the likes of Barcelona and also Bayern Munich in the last 16.
And the midfielder insists a lack of luck is the only thing holding Arsenal back from getting their hands on the trophy as he believes they have enough quality in their squad.
"I think we have been missing a bit of luck, in every sense," Ozil told Marca.
"We have been pretty unlucky with the draw in the Champions League. These past few seasons we had Barcelona and Bayern very early on.
"And even then, we still had our chances. But I think we lacked a bit of confidence against the big teams, especially in those rounds.
"It is a series of factors but we believe we can make that jump. I hope to win the Champions League with Arsenal, I think we have a team that can do it. Like I said, we need a bit more luck, but why not... we have great players.
"Qualifying for the knockout stages proves we are doing things the right way and we're on the right path. Arsenal always make it out of the group stage and now is the time to make that extra step."